The co-regency of Artaxerxes with his father is not a "theory". This co-regency began back in 474 BC. If you need archaeological proof of this, it is found in the "Annals of the World" by Ussher, who did NOT base the information for these dates on Ptolemy's canon.
The decree in the 20th year of Artaxerxes's reign is a date based upon that 474 BC year at the start of Artaxerxes's reign. That results in his decree given to rebuild Jerusalem's walls and street in 454 BC, which is the year that launched the intact, no-gap 490 years of Daniel's 70-week prophecy. The significance of this points to Christ's crucifixion and resurrection in the middle of that last 70th week, which ended with Paul's commission by God to concentrate his evangelistic endeavors to the Gentiles in AD 37. This has great relevance to you and me personally, as we are the beneficiaries of that evangelistic emphasis going abroad to the nations.
First, Ussher is not an original source for any information. Where does he get his evidence from? This is not "archaeological proof" of anything.
Now, at least you provided some actual numbers for dates. And this is what I assumed but now you have confirmed. I could never understand what Paul has to do with any of this. "evangelistic endeavors to the Gentiles" is NOT one of the 6 reasons given for the 70 Weeks prophecy in Daniel. It has nothing to do with it. This is purely made up with no Biblical proof.
Further, if the end point was in 37 AD, then you mean to say that the mid point was in 33 AD - as the crucifixion of messiah Jesus. There are many reasons why the crucifixion did not happen in 33 AD, as is commonly stated. I did a 2 part video series which outlines them all. I won't list them all here. But two of the biggest reasons that it was not 33 AD have to do with facts in the New Testament related to botany. These are things almost no one recognizes.
1. In two of the Gospels, near the time of the crucifxion, as Jesus was walking to Jerusalem, He wanted to eat some figs from a nearby tree. There were no figs to be seen. Mark gives the detail that it was not the season for figs. So was Jesus being unreasonable thinking there should be figs but not finding any? Not at all. Do some research and you discover that fig trees have TWO seasons for figs. After the winter, when they first flower, the sterile female flowers quickly develop into fruit. This is the first harvest - a smaller harvest. One that happens at the end of April. The second harvest happens later in the summer after the fertile flowers have been visited by a certain wasp that only shows up in May/June. That is the main harvest of figs that Mark referred to.
So if, as is commonly stated, the crucifixion date was April 3, 33 AD, that is MUCH too early in April for Jesus to expect there would be figs on the tree. It was actually April 25, 31 AD - at the end of April.
2. The second botanical proof is the Feast of First Fruits and the winter barley harvest. According the Law of Moses, God requires the first of the winter barley harvest to be brought to the high priest so he can wave it before the Lord at the Feast of First Fruits. This is the day after the weekly Sabbath during the Passover week (always a Sunday). There MUST be ripe barley in order for this to happen. That is why it was so important for them to begin the year at the right time. If they began the year too early, there would not be any ripe barley for their required wave offering. The entire population could not harvest and eat the new harvest until AFTER this wave offering.
Winter barley finishes flowering and begins to show green ears (abib) around the time of the spring equinox. It takes roughly 3 weeks for it to ripen properly. Again, if one considers the assumed date of April 3, 33 AD, that is MUCH too early for there to be any ripe winter barley around. It's an impossible date. It can not be correct. However, by April 25, 31 AD there would most definitely by ripe barley for the First Fruits wave offering.
So, that's the kind of research proof that is required in order to make the case for the proper date. Unfortunately, your theory has none of this level of research to back it up.