But does it, for the lack of a better word, chooch?
Yes, it chooches.
Adding the pot to test the adjustment, it turns out my BuckBlock is sourcing more than 500uA-- it's actually closer to 625uA. Also, it's firing up at ~1.5v rather than ~ 1.75v. That means I want a 2.2k low-end resistor and a lower pot resistance. So I modded another 10k linear pot into a 13k exp-ish pot, and continued assembly.
Everything goes together as intended and looks nice.
But there's a snag; I knew there was a good chance the optics wouldn't play as well with the SZH as I hoped, and in fact, the focus behavior isn't working well once on the scope. The illuminator works, and alignment is spot-on, but it's focusing an image of the lens at working depth, which is suboptimal. Also due to the suboptimal focus, lots of light is getting wasted inside the scope as it scatters out of the parallel-light/infinity focus portion of the optical path.
I'm going to have to play more with it.