Augustine would not agree with your "Reformed interpretation of Romans 9" statement. Arminianism didn't exist until about 1590 or thereabouts. I've read polls that show that only 10% of those who identify as being "a Christian" are biblically and in reality a genuine born again Christian.
But Calvinism did not exist in the Early Church (outside of the Calvinistic interpretation of Romans, and other scriptures). See quotes from the earliest church fathers.
Justin Martyr - First Apology - Ch 56-50
Chap. XLIII — Responsibility Asserted.
But lest some suppose, from what has been said by us, that we say that whatever happens, happens by a fatal necessity, because it is foretold as known beforehand, this too we explain. We have learned from the prophets, and we hold it to be true, that punishments, and chastisements, and good rewards,
are rendered according to the merit of each man’s actions.
Since if it be not so, but all things happen by fate, neither is anything at all in our own power. For if it be fated that this man, e.g., be good, and this other evil, neither is the former meritorious nor the latter to be blamed. And again, unless the human race have the power of avoiding evil and choosing good by free choice, they are not accountable for their actions, of whatever kind they be. But that it is by free choice they both walk uprightly and stumble, we thus demonstrate. We see the same man making a transition to opposite things. Now, if it had been fated that he were to be either good or bad, he could never have been capable of both the opposites, nor of so many transitions. But not even would some be good and others bad, since we thus make fate the cause of evil, and exhibit her as acting in opposition to herself; or that which has been already stated would seem to be true, that neither virtue nor vice is anything, but that things are only reckoned good or evil by opinion; which, as the true word shows, is the greatest impiety and wickedness. But this we assert is inevitable fate, that they who choose the good have worthy rewards, and they who choose the opposite have their merited awards.
For not like other things, as trees and quadrupeds, which cannot act by choice, did God make man: for neither would he be worthy of reward or praise did he not of himself choose the good, but were created for this end;52 nor, if he were evil, would he be worthy of punishment, not being evil of himself, but being able to be nothing else than what he was made.
Irenaeus in his Against Heresies - Book 4 Ch 35-38 [A.D. 120-202] shows clearly that it is man's free will choice to choose or reject God. We see this in all the Early Church Fathers.
Chap. XXXVII. — Men Are Possessed of Free Will, and Endowed with the Faculty of Making a Choice. It Is Not True, Therefore, That Some Are by Nature Good, and Others Bad.
1. This expression [of our Lord], “How often would I have gathered thy children together, and thou wouldest not,” (Mat 23:37) set forth the ancient law of human liberty, because God made man a free [agent] from the beginning, possessing his own power, even as he does his own soul, to obey the behests (ad utendum sententia) of God voluntarily, and not by compulsion of God. For there is no coercion with God, but a good will [towards us] is present with Him continually. And therefore does He give good counsel to all. And in man, as well as in angels, He has placed the power of choice (for angels are rational beings), so that those who had yielded obedience might justly possess what is good, given indeed by God, but preserved by themselves. On the other hand, they who have not obeyed shall, with justice, be not found in possession of the good, and shall receive condign punishment: for God did kindly bestow on them what was good; but they themselves did not diligently keep it, nor deem it something precious, but poured contempt upon His super-eminent goodness. Rejecting therefore the good, and as it were spuing it out, they shall all deservedly incur the just judgment of God, which also the Apostle Paul testifies in his Epistle to the Romans, where he says, “But dost thou despise the riches of His goodness, and patience, and long-suffering, being ignorant that the goodness of God leadeth thee to repentance? But according to thy hardness and impenitent heart, thou treasurest to thyself wrath against the day of wrath, and the revelation of the righteous judgment of God.” “But glory and honour,” he says, “to every one that doeth good.” (Rom 2:4, Rom 2:5, Rom 2:7) God therefore has given that which is good, as the apostle tells us in this Epistle, and they who work it shall receive glory and honour, because they have done that which is good when they had it in their power not to do it; but those who do it not shall receive the just judgment of God, because they did not work good when they had it in their power so to do.
2. But if some had been made by nature bad, and others good, these latter would not be deserving of praise for being good, for such were they created; nor would the former be reprehensible, for thus they were made [originally]. But since all men are of the same nature, able both to hold fast and to do what is good; and, on the other hand, having also the power to cast it from them and not to do it, — some do justly receive praise even among men who are under the control of good laws (and much more from God), and obtain deserved testimony of their choice of good in general, and of persevering therein; but the others are blamed, and receive a just condemnation, because of their rejection of what is fair and good. And therefore the prophets used to exhort men to what was good, to act justly and to work righteousness, as I have so largely demonstrated, because it is in our power so to do, and because by excessive negligence we might become forgetful, and thus stand in need of that good counsel which the good God has given us to know by means of the prophets.
3. For this reason the Lord also said, “Let your light so shine before men, that they may see your good deeds, and glorify your Father who is in heaven.” (Mat 5:16) And, “Take heed to yourselves, lest perchance your hearts be overcharged with surfeiting, and drunkenness, and worldly cares.” (Luk 21:34) And, “Let your loins be girded about, and your lamps burning, and ye like unto men that wait for their Lord, when He returns from the wedding, that when He cometh and knocketh, they may open to Him. Blessed is that servant whom his Lord, when He cometh, shall find so doing.” (Luk_12:35, Luk_12:36) And again, “The servant who knows his Lord’s will, and does it not, shall be beaten with many stripes.” (Luk_12:47) And, “Why call ye me, Lord, Lord, and do not the things which I say?” (Luk 6:46) And again, “But if the servant say in his heart, The Lord delayeth, and begin to beat his fellow-servants, and to eat, and drink, and to be drunken, his Lord will come in a day on which he does not expect Him, and shall cut him in sunder, and appoint his portion with the hypocrites.” (Luk 12:45, Luk 12:46; Mat 24:48, Mat 24:51) All such passages demonstrate the independent will151 of man, and at the same time the counsel which God conveys to him, by which He exhorts us to submit ourselves to Him, and seeks to turn us away from [the sin of] unbelief against Him, without, however, in any way coercing us.
4. No doubt, if any one is unwilling to follow the Gospel itself, it is in his power [to reject it], but it is not expedient. For it is in man’s power to disobey God, and to forfeit what is good; but [such conduct] brings no small amount of injury and mischief. And on this account Paul says, “All things are lawful to me, but all things are not expedient;” (1Co 6:12) referring both to the liberty of man, in which respect “all things are lawful,” God exercising no compulsion in regard to him; and [by the expression] “not expedient” pointing out that we “should not use our liberty as a cloak of maliciousness,” (1Pe 2:16) for this is not expedient. And again he says, “Speak ye every man truth with his neighbour.” (Eph 4:25) And, “Let no corrupt communication proceed out of your mouth, neither filthiness, nor foolish talking, nor scurrility, which are not convenient, but rather giving of thanks.” (Eph 4:29) And, “For ye were sometimes darkness, but now are ye light in the Lord; walk honestly as children of the light, not in rioting and drunkenness, not in chambering and wantonness, not in anger and jealousy. And such were some of you; but ye have been washed, but ye have been sanctified in the name of our Lord.” (1Co 6:11) If then it were not in our power to do or not to do these things, what reason had the apostle, and much more the Lord Himself, to give us counsel to do some things, and to abstain from others? But because man is possessed of free will from the beginning, and God is possessed of free will, in whose likeness man was created, advice is always given to him to keep fast the good, which thing is done by means of obedience to God.
5. And not merely in works, but also in faith, has God preserved the will of man free and under his own control, saying, “According to thy faith be it unto thee;” (Mat 9:29) thus showing that there is a faith specially belonging to man, since he has an opinion specially his own. And again, “All things are possible to him that believeth;” (Mat 9:23) and, “Go thy way; and as thou hast believed, so be it done unto thee.” (Mat 8:13) Now all such expressions demonstrate that man is in his own power with respect to faith. And for this reason, “he that believeth in Him has eternal life while he who believeth not the Son hath not eternal life, but the wrath of God shall remain upon him.” (Joh 3:36) In the same manner therefore the Lord, both showing His own goodness, and indicating that man is in his own free will and his own power, said to Jerusalem, “How often have I wished to gather thy children together, as a hen [gathereth] her chickens under her wings, and ye would not! Wherefore your house shall be left unto you desolate.” (Mat 23:37, Mat 23:38)
