Assuming that you have full Tradition and Aesthetics, and then some other policies that give specialist buildings... on a very Late game, how high must your population be, assuming a fully built and very impressive capital on Info era, to fill in all those specialist slots and then work some tiles?
On my Japan Trad/Auth/Aesth game (yes, abuse of GP) I never have enough population on my Capital and satellite Culture cities to work all the slots. The cities have nice food and no AI dares to pick a fight with me for long since it's a small continents map(I have a small continent for myself) due to my nice navy and coastal defenses. Problem is, I have vast swathes of unworked tiles cuz most of my cities don't have the population to support both my specialists buildings and my nice desert farm land... How should I balance specialists and population growth? I'm planning to restart that game and I'd really love some advice... Should I settle cities at the minimum range this time?
P.S. I said desert farmland cuz the lower half of my continent had vast deserts with a river, 2 oasis, and lake Victoria nicely spaced on it. Then I plopped down a city in the sweet spot and built Petra on it. Any desert tiles w/o fresh water were mined/manufactory/academy'ied
Also, should I give up Town chaining for farm chaining? there were a few coastal tiles where I placed my roads and they had freshwater on it...
Completely depends on how the rest of your land looks. Eventually if you choose to adopt the freedom tenet that halves food cost for specialists you're probably going to work all specialists available anyways, but in general this is a place where you have to make a decision, do I want yields now or do I want the city to grow so I can have more yields later on?
When I play tradition I try to work all engineers and all cultural specialists in the capital, while focusing the city on growth as much as reasonable, this usually ends with me having to add merchants because my economy is failing and scientists because I'm falling behind on science . Seriously though, the more you can grown your cities the better, my non capital cities usually just work engineers, or no specialists at all if good mines are available, I mean getting those essential buildings up is just as important as growing the cities.
As far farm-clusters versus villages go, I'm really out of touch with that subject, I tend to build as many villages as I can reasonably fit, but that's because I'm running the extra events mod-mod that generally tend to strike you down with a '-1 food on all farms for the rest of the game' event fairly early on, and after that farms just feel weak. In general I believe that farmclusters are superior to other improvements, and for that reason you should probably build the villages you want on hills, but a lot still depends on the situation.
From your explanation is sounds like you've severely neglected your growth and is paying the prize for it.