This is a question I asked myself years ago as well. What really helped me to think about different strategies was the following topic
and the reply by @cl2488
From less to more radical: I've proposed for not all to have basically the same Storehouse techs (just the names are different, I think), this would give more variation on how each civ would obtain and trade resources. I haven't carefully checked the other economic techs among civs, but all that is an opportunity to add variation. The same regarding religion, that being something that should be quite different among civs, and luckily many current temple techs lack decent names and icons, giving ample space for change and (needed) improvement. I've mentioned that all civs could have their very different special units, like the Ministers are for the Han. Also, the naval system I proposed is actually not that radical (after boarding is implemented) and gives more opportunities for strengths and weaknesses, thus each civ would have a more characteristic, interesting and historically accurate way to do things at sea (which right now it's something quite avoided, when it could be fun, as it has been in some Total War games).
I hope your problem is solved nowadays, but if not I really recommend you and everyone finding this topic in a research: Try using ethernet! (I know it's like IT Helpdesk telling you to restart your PC first but using WiFi for multiplayer matches via lobby is a very common root for problems.
I totally agree ! There aren't really any major gameplay differences between two civilizations, apart from slightly different units and a few bonuses... I'm currently working on a mod that will (I hope) almost completely overhaul the civilizations, including the addition of slaves. I hope to release the first civilizations before November 1st.