Doesn't really help me no offense. Trying to find out how/who to transfer these domains too and if it's possible to avoid paying $800/year to name cheap. Do you know any providers or if this is possible, concretely? I cannot find any information one way or the other.

I think the best you could do would be to get Namecheap on the phone and ask them what they can do. This is not a regulatory issue, but rather a business negotiation. The registrar will accept whatever they can get out of someone for a domain. You could try talking to a few registrars and see if they can help you out. Provided you have the unlock code, it's up to the registrar to accept the transfer and agree to accept a payment for the domain. I don't really have a better answer. Perhaps someone else here does.

After some more digging it looks like prices are set up by some "registry" that the registrar has no control over, so it'll be the same price everywhere. I don't think what you wrote is correct.

What is this registry?

The owner of the top-level domain. With the new gTLDs that got sold they are quite free in coming up with their own pricing models.

I think ICANN?

That is unlikely. ICANN has set fees per TLD that are very low. The registrars are the companies that jack up the prices. You should make them provide you a source for who is setting this price. I think they are pulling your leg.

If a registry wants high prices for it's "premium domains" (whatever it defines as such) on one of its TLDs, the registrar can't magically charge you less unless they are willing to make a loss on you. ICANN doesn't really restrict the pricing the registry chooses for this class of TLDs (afaik the contracts for older ones like .com/.org/.net have such limits, but not the new gTLDs, there the registry can do pretty much whatever if wants).