It's problematic to link you to anything, if you don't have any concrete questions.
From what I read in your post, I fear, that you might neglect the power of cottaging your capital and running Buro. Specialist Economy is an outdated term, nowadays all players run hybrid-economies, so they mix the sources of economy for an overall maximum, and don't only resort to one.
Also, Philosophy, unless you need it as tradegood, is a completely useless tech to research on your own if you go for a Cuirrassier rush. You might need to, because you need it for Lib, but you shouldn't research it for the Religion, but bulb Education instead and trade for it, like that you'd have earlier Cuirrassiers and would get it for free, while only missing out a holy city, which you can easily conquer with Cuirrassiers. Going for a mid-game Religion is good, if you're in an extreme underdog situation, because then, Philosophy is awesome tradegood and you could use the holy-city-bonus together with a different state religion for 40% cheaper tech-steals, and as tech-steals are already cheaper than teching something yourself, that'd be a great choice in the scenario where it's impossible to compete in GNP. The advantages available from getting civs towards friendly (which usually needs either the same or no religion) is probably the biggest advantage in the whole game, as tech-trades are the biggest source of BPT on the higher levels. Also, if you can bribe AIs into world-wars, then you're safe and can backstab them easily.
From the last sentence you ask for very sophisticated strategies though. Idk if you already did this, but definitely read the CIV-illustrated guide on hybrid-economy and the writeup "Replay #9" (links in signature) . In Replay #9 I played with Montezuma on a Boreal map and used the SPI to a maximum extent.
The only thing else I could give to you from that question, is the simple mechanic, that the number of population is the important factor when it comes towards religion, so always spread to the biggest city, and if you steal something the way I described, spread religion towards that city first aswell (see example(s) in Replay #9) . You can gift the missionaries towards the AI once you're in their territory, like that you save turns and can spread your religion faster, AI always spreads to the biggest city. AI needs a certain amount of population, before it is willing to switch its religion, and AI always prefers self-founded religions in the case, where two religions should be equal. I'm not exactly sure about the speed at which AI switches, but I think it was a max. of 5 turns if SPI, 10T if not and in peace and 20T if not and in war, so that's the time AI afaik will stay in the religion you bribed them into. Completely converting AIs by spreading religion towards all of its cities is too costly, as you could probably conquer it with those resources + a few more.
And regarding diplo in general: I calculate diplo. BUG + BULL or BUFFY .004 are great help in this. I believe friendly is +10. Not 100% sure about the last, because I still play with BUFFY .003 and that one doesn't show the hidden modifiers. Best article on diplo is CIV Illustrated #1 (also signature) , though that one is a pure reference book.
Hth, and I'll notify a mod to plz move this to Strategy & Tips, because you'll get more answers there.