I did some more poking around and I eventually discovered that my drivers automatically assigned an energy savings profile to Black Ink, which overwrites any handmade profiles. Normally I only see this happening with native Windows programs (otherwise it asks), so I had no clue. Popped it back to high performance mode and everything works like it should.
For reference, my setup is a Radeon 6520G + 7670M. The former is an integrated card, part of an APU, and can't be turned off. In other words, either I run software purely off my integrated card*, or I run both in crossfire. Sometimes it doesn't make a lick of difference, but with Black Ink I'm getting roughly double the frames now.
But that's not all, I also noticed Black Ink seems to run with v-sync on by default. Not sure if that's a driver thing or a software thing, but either way forcing it off makes my fps skyrocket. Where it was roughly 60/20 fps (idle/using large brush) before it's now 170/65 fps. Secondly, using the D3D friendly crossfire profile turns it into a neat 200/80. Finally, turning on driver-handled texture filtering (aka Catalyst A.I) gives me another boost of 40/20 frames. Lag be gone! That's a pretty huge fucking difference, I'd say.
* For future reference, this stopped being the case in a later driver release