Well, first of all, your interpretation of Scripture IS subjective. Even more subjective than a review of the evidence from God's Creation can be. That doesn't mean your interpretation is necessarily wrong, but to deny that your human subjectivity is not involved in how you read Scripture is to make a fairly dramatic proposition that even Augustine refused to make. So, the choice is NOT between subjective review of natural evidence v. objective truth of Scripture. It is, in the case of origins, a choice between subjective, but testable and methodoligical, review of natural evidence v. subjective review of Scripture.
What you have done is start with a subjective interpretation, Then convert it into an objective Truth of Scripture, then use that new status to trump everything else. The point is that just because we believe something to be true in Scripture, this does not make it absolute truth. As you have pointed out, outside of the essential salvation issues, things are often (usually?) subject to various interpretations, and thus we have to choose among them, prayerfully and with the Spirit's guidance. But we should remain as humble as Augustine about such choices. Yes, we should make a choice, but only believe it with the degree of certainty that is consistent with a review of all of those factors Augustine mentions.
If you believe that the best interpretation, taking all these factors into consideration, is that the earth is young, then fine. But since it is not a salvation issue, it is not wise, IMVHO, to hold such a belief dogmatically or, worse, treat it as if it is suddenly an objective Truth of Scripture, which would then require absolute refusal of all that would contradict it. I think that belief should be held only with that degree of certianty which is warranted by all those factors.
But your proposition is not completely true on the science. There ARE alternatives. You could still believe that the earth came into existence 10,000 years ago even if you didn't have the Bible to tell you that - if all the natural evidence pointed to it. After all, even atheists believe it started at a given time. If the evidence really is that the earth is young, then you would simply think that starting point was more recent rather than later. The question is whether the natural evidence, on its own, points to a young earth or an old earth.
Right now, you seem to believe that there is a great deal of convincing scientific evidence that the earth is actually about 10,000 years old. If you (somehow) found out conclusively tomorrow that either an old earth or a young earth could be completely consistent with Scripture, and you could, in good conscience, come to either conclusion based solely on the natural evidence, would you conclude the earth was young or old?