Sorry for the slow response, I was out of town over the weekend and had just gotten back.
I'm using mainly my Friedman 2x12, loaded with V30s, Sometimes I do use the same setup with my 2x12 Mesa (Stock) or 1x12 Marshall 1912 (Stock), they do sound slightly different, and I would have to tweak the global monitor EQ settings a little to taste depending on the room situation. Using different tube amp head power amps and different cabs will impact your sound, and I normally just go to my global monitor EQ settings for a quick tweak. I think it's just like tube amps as well, when you go to different venues or locations, you will have to make slight adjustments to tastes.
You are absolutely right that if you spend allot of time tweaking, your ears will get tired or used to certain frequencies.... then it's a constant struggle to get back on the right paths. It's always good to walk away or come back the next day to continue. That said, tone chasing never quite ends for us guitarists..... 
I know that I said earlier that by adding the EQ and filtering out the frequencies you don't want, there's more to it than just that. I spent allot of time also tweaking the amp block settings to get what I want. Since I have use two tube amps (Freidman JJ 20 Jr. & Mesa Express 5:25), I used them as references and A/B between the profiles and amps, to get as close as possible. It's never 100% but in the ball park. Once I'm happy what the results, the live setup is easy, consistent, and never have to worry about mic placements or other issues that comes with it.