Turn-based is best for single-player games. After all, with multiple people, you end up waiting for somebody to take their turns. If turns are sequential you end up a lot of time waiting. Real-time is generally a better fit for multiplayer.
Agreed. Turn-based, especially sprawling lots-of-choices like the 4X genre, don't work particularly well in MP. Instead you ideally need to move to simultaneous turns.
Or be like the forums hounds who play 1 turn a day and analyze EVERYTHING.
Personally I would move to Tabletop games (or Boardgames). They're much better designed for short turns with interactivity so there's minimal downtime for players getting bored.
That being said, if you're looking for Civ5 but on mobile with Multiplayer, UnCiv is a FOSS project for Android, PC, Linux, and Mac w/ Java. Moderately vibrant MP community on the Discord.