I don't think the Dome thing is a factor separate from the H/A issue which I already discussed and adjusted for. The team gets 2.82 PPG at Home and 1.00 Away. Dome is 4-0-0 at Home and 0-1-0 Away. If you adjust or both H/A and PV/Dome, you're adjusting for the same thing twice I think.
But as I initially wrote, I do agree the W/L is not the whole story: opponents, the rest of the lineup, and other factors you mentioned are relevant. I also explicitly did not claim that the W/L record proves the team is better without Villa.
But, some things you mention, like whether the team relaxes when he starts and steps up when he's out -- those do not disprove the theorem either. They just maybe show it isn't Villa's fault. The team can be better without him without him being to blame.
Finally, circling back to Dome and H/A, this reminds me to mention that I think people make a mistake when they say the club is better under Dome because we won 3 in a row after a long period of uneven results. I think we're better because of the eye test. But in terms of results, all Dome has done is not lose a home game. PV was just as good at that.
I think the Dome difference are the in game adjustments we’ve seen. And also willingness to not play purely out of the back. I’m not sure PV goes 3-0 at home vs those opponents and sticking to his one and only strategy.