Keep fleets stationed at different point near enemy ports so you can do the easy blocade missions to keep the senate off your back. It's difficult to do every conquest mission though, and it's no big problem to miss a few.

Edit: remember to drop the blocade immediately so you can do it again later...

The other day I conquered Petra for the senate in my last mission before the civil war. I managed it 1 turn before the limit. If I didn't do it the senate would "reveal my secret". They get rather nasty as you grow bigger.