To fix the game flow issue, I am considering just mashing two base game sets together, so there are two copies of every card. It seems like that would give you the team flavor while still keeping the pace/pile depletion still at the rate of an ordinary 1v1 game. Of course, it requires I am willing to basically lose two sets, or to fish them apart for 1v1. But hey, base game innovation is so cheap anyway, right?
The other thing I dislike about the team game is how much symmetric sharing of a symbol ends up being important. If you and your teammate both have say, exactly 5 crowns, and you keep on sharing some crown tech, you really start owning. Maybe one way to fix it is that your teammate can share your dogmas only if he has strictly more of the symbol than you have to break the symmetry.