Galdred
Studio Draconis
You can also set a disciple game with 2 pretenders, and voila, no more diplomacy problem!Dominions is a great game, can recommend for the type of game you seek.
Be warned though, it becomes quite a time-sink later on, and if you lack charisma (or desire to put your charisma to work) then other players quite often gang upon you and start a slow, agonizing suffocation that can last for dozens of turns (i.e. dozens of hours). A great game, as you can see.
Master of Orion with no battle is simultaneous asynchronous.
I agree it is the most conveient way to play, but it is also badly under represented
There are some online games that could work you:
Neptune's Pride was a Diplo focused 4X in space. You can play either in no sleep mode (1 movement tick every hour. Good luck with managing your winning/sleeping balance!), or in turn based (1 turn every 8 hours iirc).
It is rather nice, as long as you stay away from the large games where you discover in the end that several players entered with 5+ accounts.