I'm far from an authority about this (or about anything circuit-related), but I've spent a lot of time fiddling with my BeePre to lower the filament regulator dropout voltage. Here's a thread detailing my misadventures:
http://forum.bottlehead.com/index.php?topic=11727.0Based on my experiments and fuzzy sense of how the fil reg works, I don't think there's a way of preventing dropout and resulting hum if your wall voltage is dipping below, say, 115VAC, unless you're willing to make some biggish circuit changes.
Subject to what PB or PJ say, I think there's a tiny bit of wiggle-room with the voltage divider that sets the POSout voltage. I believe that if you decrease the POSout voltage by tweaking the divider, the regulator will have more compliance (excess raw DC input voltage) and this will give you a slightly lower dropout point. Downside: you change the bias/operating point of the 300Bs. And, just guessing here, this might give you maybe an extra 0.5V of wall voltage sag tolerance before dropout occurs -- i.e., not much. [Edit: I forgot to mention that if you lower POSout, you'll have to tweak the value of the cathode resistors to keep close to 5V dropping across the filament]
I suspect the easiest solution is to continue using the variac. Other options, in increasing order of fuss/difficulty:
(1) Add an autoformer in front of the BP that bumps your incoming mains voltage to around 120VAC.
(2) Add new filament trafos with a crc or clc filter so that there's less ripple at the input the fil reg. Based on my experiments, more input ripple = less compliance = higher dropout voltage. Less input ripple = lower dropout voltage. With my CLC filter, I can go as low as 108VAC wall voltage before dropout, and even with dropout the hum is fairly minor. The challenge will be making all this fit on the stock chassis. I rebuilt my BP in a much bigger chassis.
Just some thoughts. Hopefully not too erroneous.
cheers and good luck, Derek