You've researched Engineering since posting? I thought you were still in the AA? Maybe I missed that. I thought you were a tech short of the Middle Ages, missing Currency?
My advice, revolt immediately. If you are not going to research anyway, forget Republic and go Monarchy. The beauty of being religious is that you can just swap later for 1 turn wasted and go with something better. Getting out of despotism is priority #1.
I think you could get away with low culture - I usually build some markets/libraries/auqa/harbors even in a war game but I've never been given an award for a fast conquest! Of course you have neither Lit nor currency (IIRC) so no libraries or markets! At least not yet. I woud be tempted to up temples ONLY because we need some culture, we are a religious civ, and if we are not going to research then they are cheaper and come with a happy citizen & cuture for the upkeep. Either that or start dropping more cities! CxxC spacing!
Another option that I didn't explore was who has the ToA. If you can capture that for the free temples, even for just 5 turns, that will solve the culture/border problem, at least for a while.

Another thought - since NO ONE has bothered with literature yet, you could shoot for the GLB and then coast on the other civs until education. I think the AI you have will go for MT before Eductation. Not sure on that, though. Korea will probably go for metal fast for their UU. Dutch and France are wild cards. No one else has the muscle to do any research.
Bottom line, though, is more workers. I understand the desire to put off the workers, but if your population is working unimproved tiles how much are they really worth anyway? You can't do without improved tiles at least around your core half-dozen cities. By 10AD you should have major infrastructure up and running and even without water in your initial cities, you have some okay land (not great by any means) around to push out settlers and workers. That's more about how you got here than what to do now, though.
One thing I noted was that the only embassies you have are with the Civ's you've pounded into the dirt.

You'll need to spend some gold to get those allies. I though about that. Considering your extra luxuries, if you can get an embassy with say France you could have an ally. It will also weaken France so that when you attack them they will have either wasted their units or sent them to the other end of the world.
Only problem with calling in allies is worry about the Dutch gobbling them up and becoming a monster. Even so I would not be overly worried. Push out more workers to improve the land and put up your FP. I don't think I saw it in any of your cities.