Well since it seems doing something about the AC seems to be the only option, I've been looking into that a bit. Seeing as the epislon-24 shuts off every time I turn on certain electrical equipment, I assume that short AC drops are the cause, so I looked at getting a UPS. From what I could read, there are 3 main types - offline (only activates when AC goes out of acceptable bounds), line interactive (corrects AC up or down if AC error is small, shifts to battery if AC error is large), and online (always using the battery).
The issue is that I don't know if the UPS will correct the voltage drops quickly enough that the epsilon-24 won't shut off. I read something about them taking in the order of 5 milliseconds before activating. The online UPS is noisy and expensive, so I'd rather not get one of those, though they have an activation time of 0 s.
I also thought about whether it would be possible to just connect some kind of battery to the circuit, so that it would always have a reserve, and it would be a bit silly getting a big UPS for the whole pre and power amp system, as it's only the epsilon-24 circuits that are vulnerable. I realize that this will remove the over/undervoltage protection, but at this point I'm exceptionally tired of them shutting off all the time.