> there is an overwhelming amount of evidence that many if not most of those particular claims are false

Most, but not all, of these claims are, theologically, untestable.

Here's an analogy: Would you find a guy walking down the street, ask him to take part in your science experiment measuring how high guys can jump, hear him say "no I don't want to take part", then conclude that because he did not jump for you he is unable to jump? You wouldn't. In fact, you might get disciplined by your university's ethics review board for experimentation without consent. In the same way, for most tests, the Bible says that God does not want to be tested. You should assume that your unwilling test subject will not cooperate, or even work to frustrate, your tests.

The talk about observations over longer times can seem persuasive. I think an analog would be hiring a PI to tail the unwilling guy test subject for years. But if you don't see him jump in 5 years, does that mean he can't? What more if he knows you're following him and that you want to see him jump, is years of not jumping valid evidence then? That's not evidence at all, much less overwhelming evidence.

As an agnostic, this is a topic that greatly interests me.

One challenge I've found in navigating this is determining the extent to which (interpretation from an untrained but intelligent layperson) == (interpretation from someone with a lot more historical, linguistic, and theological training).

I.e., how much research is needed before one can reasonably conclude that the "promise" being evaluated isn't just a straw man.