Here's how it all went down:
Trial and error and wack-a-mole trying to enable the rest of the buses while still keeping VEP happy enough to produce sound. The other "offending" bus that needed to be pulled out and placed in its own Server Instance was INSTR STEM. No idea why. It seems very arbitrary. There didn't appear to be anything special about INSTR STEM compared to its sibling Group Channels.
The other piece of the solution was to continue connecting Audio Inputs even as it was continuing to fail. In one case (one Server instance), no sound would be heard until all the connections were made.
In some cases, in this game of wack-a-mole, an offending Audio Input would disable all the audio. In other cases, only some of it. Again, I was not able to figure out why.
The other part of the solution was to try shutting down Cubase and reloading. In some cases, where no sound would be heard, this would restore sound. That "step forward" has in all cases seemed to "stick" and on subsequent loads; everything works.
My intuition as to when to try out this time-consuming test (the Cubase project takes around 8 minutes to load), became somewhat of a black art and I'm not sure I could reproduce it.
But now that it's done and everything is wired up, this should hopefully be a one time deal. If it survives product updates and further useage. We'll see. If the connections continue to stay solid, like they are now, it will have saved me a ton of money on hardware. If it doesn't, VEP is a relatively small price to pay and will surely find other, more normal uses (like offloading virtual instruments).
So, for now I'm going to call this "Solved, mostly."
I should also note that it is really not properly "in sync," strictly-speaking. If compared to the internal metronome track, it's off. But because all the final stems are all out of sync by the same fixed, VEP buffer amount, it's in sync for all intent and purpose. This solution would not work for someone wanting to, say, just process a drum bus. It's an all or nothing affair.
Again, an Audio Insert version of the Audio Input would likely solve these issues by allowing the DAW to do its PDC thing properly.