Well, I finally played a game out a little more peacfully so I could experience the late game. So I have a few new observations, minus the stories of my conquests this time.
First, the tech rate in the mid to late game is insane. With moderate trading with the AI I was out of things to research by about 300AD. This meant that I would either pull in close to 3000 gold per turn from then on, or I would build 70 culture per turn at my smallest cities, 200+ at the largest. Your idea of some techs that can't be traded is a good start, perhaps you can expand that list while at the same time increasing the cost of the those techs since you have to research them yourself.
Commerce is a bit too plentiful, I know it's been mentioned before so I'm just confirming it. It's pretty good early in the game, reaserch isn't too quick and gold is hard to earn, but as you continue to develop better tech giving you additional trade routes and buildings giving you a substantial increase in trade route yield it gets pretty crazy. This is also perhaps related to the holy shrines with their additional gold per turn, especially with christianity because it spreads like wildfire and I know you were talking about changes to those as well.
Despite the great unit variety I find myself only using a very small handful of them. So many of the bonuses are either useless or just not good enough to make one unit as good or better than another of the same period. I would suggest scrapping most of the "built in" bonuses that have been added to the units and letting the player's choice of promotions dictate what their units are good at, the AI does quite good with selecting appropriate promotions as well. Some of the UU bonuses could be handled the same way, with a free promotion. I don't think the upgrade options need to be removed for any of the units, but perhaps they could be a bit more expensive, maybe change the per production cost to 3 (or even 4) and reduce the base upgrade cost so it would be less expensive early on but substantially more expensive for the later game units.
Also, some of the unit bonuses are a bit too good. For example any of the spear/pike units receive a bonus against cavalry and mounted skirmishers. They should really receive no bonus against a mounted skirmisher and a defend only bonus against cavalry (you can do that, but it has to be a unit_class modifier, not unit_combat).
The bonuses against siege weapons are effectively useless since siege weapons have such low strengths compare to other units of the same time period.
On the AI their "memory" seems to last forever. So if you make an enemy early in the game they're probably going to be an enemy for the entire game or until you eliminate them. What I saw happen was that I ended up being most friendly with the empires furthest from me, not because of close borders but because I hadn't declared war on their friends. Rome, for example, had a -8 "You declared war on my friend" by 200AD as a result of several small wars with some of my close neighbors. The result is a fairly static diplomatic enviroment, the AI either hated me or loved me with nothing in between and there was little I could do about it. I also found it odd that even though so many of them hated me for starting wars with their friends, only one of them ever declared war on me. Parhaps a lot of the negative effects could have their "strength" increased but their duration decreased, so they'd get more upset at the time of the action but an earlier action would have less effect on the later game. This may be just enough volatility to get the AI really kicking off their own wars without being quite so player-centric.
I would increase the effect of demanding trubute, refusing to pay tribute, refusing to help in wartime, declaring war on a friend, stopping trading and trading with an enemy. If you do reduce the positive effects of religion as discussed earlier I would also consider increasing the positive effects of good trade relations or helping/paying tribute.