Except it isn't that hard on Epic, let alone Marathon which a lot of players use, and it would be actually almost impossible on quick, bar some crazy husbanding of unit, to carry over a woodsman promotion. That is why every other mechanic uses game speed scaling. Getting attached to a single number because of some vague historical factoid is silly, when it throws off the game balance so hard.
And that rationale makes the Eagle a even more lacking UU, if playing 'as intended' on standard. I've barely used the free workers it gives, because I've largely already bought workers from the gold my Jaguars farmed. And I'd be getting them even later, as non experienced units who I have to research then build, then deploy. The main worthwhile aspect of Eagles, is the elite upgraded ones, not their particular actual abilities.
And this means that there is barely any incentive to keep Jaguars around, and instead might as well upgrade them to spearman, bar a few that would have to be carefully husbanded to be the finishing blow.
Anyway
@Jiggly I really don't know how you are having trouble hitting religion with Aztecs and God of War. I've found it easy to found with Aztecs non 3rd and 4th modded on standard with Goddesss of Protection (missed God of War) and even easier modded as both a Wide Empire and OCC with God of War on Epic. Are you playing on Quick?
Aztecs and God of War is honestly the quickest reliable path to a religion. They are one of the few civs that can found in the Ancient era, with no luck with natural wonders or city states.