It's been a minute, but today I realized something I should have noticed long ago.
We don't need to wish for this, the Multiplexer block IS an 8 channel volume control!
Its main purpose is that it can select from 8 different inputs (really 8 different matrix rows), but each of the EIGHT channels has its own independent volume too.
Most blocks don't have 8 separate channels, but this one does.
You only get two multiplexers (on the Axe III, don't know about FM9 or FM3), and it doesn't solve everything, but it's enough to do some of the things I want this for, mainly a single amp channel with a bunch of different drives that may goose volume enough to want to compensate.