You can turn off the Hugo M scaler and turning it back on and it will be fine - there is no warm-up time on the scaler. Curiously, I used to think that there was maybe a 10 minute warm up time on the Hugo 2, as on flights it takes 10 minutes for the best sound - but repeating the test when in a hotel room at NYC canjam I could hear no change after 30 minutes when playing back the track I used after turning on Hugo 2. So the change when flying is most likely my ears getting used to the pressure change.
I always use the battery when flying because it will work. The mains on planes often do not work or are not turned on.
On short flights in economy (2 hours say) I just stuff the scaler in my man bag with the battery. After two hours it gets a bit toasty, but the thermal trip has never been triggered - I put the thermal trip in because of this mode of operation. On long haul, premium economy, (prices on business class has sometimes been outrageous recently) I choose a window seat, and lean the battery, Hugo M scaler and Hugo 2 against the wall. In business you have plenty of room to site the gear.
A battery on the AP will be the same as a short, i.e. 800nV - absolutely nothing like those measurements which are hundreds of times worse. And anyway, the SQ issue here is 2GHz ground loops via the mains, for which you can get complete isolation with a battery and an optical input.