Evaporation has less to do with temperature, and more to do with the humidity level of the air.
You don't need to leave the cover off when you add Ph adjusters if you dont' want to. Good idea when adding chlorine, but other than that, nah.
You're worried about loosing 1/4" of water per week? If your using the spa regularly, I'd say it's not a concern.
You seem to be getting a little obsessive on some of this stuff. Relax and enjoy your spa more, and worry less.