Current SVN, checking.
Research:
Worldinfo.xml; iResearchPercent
Increase them. Try
From Duel up: 100, 110, 125, 145, 170, 200, 250.
The BBIA (iTechCostModifier) in Era Info can be used to tweak extra. 0 = 100%, 20 = 120% of research beakers needed, increase until satisfied. I use what is in my handicap taht you got with the other files if you want o check what I did. I also set iResearchPercent to 100 on all, feeling taht to do double changes (both reduction in science output and increase in beakers needed) is overkill and makes it harder to actually set and see changes properly.
As for the costs I think I know. The NIMBY buildings (are you running with auto-build NiMBY/YIMBY in "my mods", I think you are as the AI has the same trouble) are high cost/low gain buildings you do not really want in all your cities, not does the AI. Those
have to be checked and any high cost buildings, i.e. increased maintenances, need to be
not autobuilt.
Removing Graveyards, Sentry Posts, Crusifiction Crosses, Healers Hut (except for the Healer's Hut in your capital) in your save makes your gold at 100% science go from -44 to -14.
The AI will have the same problem and will explain why it is not expanding. It can not run a good economy with NIMBY/YIMBY MyMods on with proper maintenances.
You also have expanded faster than your ability, despite the Civic stating "more than 6" as that city limit no longer is what you can expand to.
You also have 2 cities far, far off for your map size this early, costing 6 and 5

in distance costs already.
If you abandon Nippur (or never built it if you go back one turn) you are at -2

at 100% science, and have a maintanable nation for your size. A couple more

buildings and you are on the right track.
Before settling new cities you should have a good economy, like going green by a fair amount, otherwise increased costs will have you struggling, which can be fun too, if you want to try that.
If you want early game to allow more cities faster, which I am not so sure about, then the WorldInfo maintenance numbers can be tweaked down a bit, but the flipside of that is way, way too manby cities once you reach Classical Era and Republic Civic, like 40+.
For me the beginning is not about spaming cities but building up the few one has, exploring, getting to know and spy on new civs, neighbours, and the science one gets.
Anyway, that's what I find from your save.
Cheers