I'm trying for a domination victory.
"For military victories, it's not necessary to switch to Communism"
I usually use Republic for the middle ages, but I always have huge swaths of completely corrupt cities. Although they make good specialist factories, I find that, upon switching to Communism, techs go from taking 5-6 turns to 7-8 turns, then quickly drop to 4-5 turns as I build libraries and universities in my former specialist farms. Additionally, Communism lets me support a much larger army. Also, being religious, I can switch with a minimum of fuss.
Let me preface this with a
caveat. I still have yet to play Communism. I rarely play religious, so switching to Communism is a big headache for me.
That said, I also wind up with lots of 90% corrupt cities. Those are my farmlands. I have put two games down in Stories & Tales: (a) The Unluckiest Lucky Start; and (b) Awn of an Ynasty. Both are Monarch-level games. The first (IIRC) ended in a domination victory and I'm shooting for conquest in the second. In both cases, I stayed in Republic the whole time.
In Unluckiest Lucky Start, I could have researched The Corporation in 5 turns at 0%.
See Chapter 16. I did go ahead and bump research to 10% just to get it down to 4 turns.
In Awn of an Ynasty, I was able to research Sanitation (a tech that I almost never research) in 4 turns at 0%.
See Chapter 16. (Wow. Up until now, I never realized that both of those events occurred in Chapter 16 and that, in both cases, I was researching 603 bpt.) I was also paying 0 gpt in unit costs in each case.
I say this, not to brag, but to point out that there's no need to switch to Communism (incurring anarchy) and expend shields on libraries and universities to keep up in tech. If I understand your post correctly, you're doing 5-6 turn research in Republic. In order to get Communism to turn research at a comparable rate, you've got to build more libraries & universities, and pay the attendant maintenance. I'd rather spend the shields and gold on artillery.
As for supporting a larger army, frankly, warfare in Republic is about fighting smarter, not harder.
"nor to build temples and cathedrals"
I usually build temples for the culture, and cathedrals to keep my size 12+ cities from rioting. In republic it would seem especially hard, with no military police and war weariness. Is there another more efficient way to keep people happy?
I'm going to hazard a guess here: I'm probably dead last in culture in most of my games. I don't usually go for culture victories. For me, domination games usually turn into an exercise in razing cities and planting settlers to capture tiles.
As for WW, as I said above, Republic is about fighting smarter, not harder. It's about managing losses by using terrain and artillery units, buying luxes, making the other guy DOW you (rather than the other way around), and fighting oscillating wars.
As chrisman1 said, "luxuries and marketplaces." They go a long way towards keeping people happy. I'd also add that I rarely have cities over size 12. Like I said, I rarely research Sanitation. I don't have to deal with as much crowding unhappiness and no pollution from overpopulation. On the other hand, with a more densely-packed core and large stretches of farmland, I usually wind up with lots of cities to manage.