If I can't get this thing to come to life in its current configuration, I'll try moving the drive to an external 5MB ProFile case with a known good controller board.
Well, good news and bad news. The good news is that it's working. The bad news is that the original Seagate ST-506 wasn't useable, and wouldn't even attempt its power-on self-test in an external ProFile case. I had several loose ST-506 drives from old ProFiles and one ended up working. On the controller board, I had to change one PROM (Apple PN 341-0067, that was getting way too hot) and change the Synertek Z8-03 RS out for a working Zilog Z8603 RS. Once those were swapped out it started behaving exactly like a regular, external ProFile. POST completed successfully, and BLU sees it as a regular old ProFile.
The "Pepsi" ProFile controller board and the aluminum shelf are all that's unique about this solution. The bog standard ST-506 (or ST-412) is the majority of it.
I have to wonder why Apple went to all the trouble of engineering and manufacturing a 10MB Widget, given this setup seems to work just fine. Were they having major pricing issues with Seagate?
In any case, maybe I'll be able to convert it to 10MB at some point thanks to Alex's insight (thank you!)

Edit: I also refurbished the Sony OA-D34V 400K floppy drive. Cleaned all of the hardened grease and lubricated it, and washed the leaky capacitor juice off of its circuit board. Seems to be working fine now. I can't help but wonder what the "
AMV" label above the "September 1983" date sticker means. Apple Macintosh Variant? This would have been around the time Apple was integrating Sony 400K drives into the product lines. Hmmm...