Evaporation has less to do with temperature, and more to do with the humidity level of the air. Â
You don't need to leave the cover off when you add Ph adjusters if you dont' want to. Â 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.