After considerable stalling, I filed the heads of two brass 4-40 screws down to about 1 mm, leaving just a hint of the slots in place. They’re a bit over 5 mm in diameter, smaller than the 7 mm I wanted to use, but have the compelling advantage of being Close Enough to get the rest of the hardware working. The gap between the interface PCB and the case is 3 mm, which turns out to be just about exactly the thickness of a 4-40 nut and flat washer, so I soldered a pair of them together as threaded spacers:
The soldering looks worse than it really is; they’re secured all the way around.
For the external battery connectors on the top, I ran a #33 drill through a pair of miniature crimp ring lugs to get a slip fit, then soldered them atop a pair of nickel-plated nuts. In normal use they’d be captured by the nuts, but I can’t figure out how to assemble them inside the case:
Those are stainless steel 4-40 screw cutoffs, which I used because solder doesn’t adhere to stainless… I tinned the nuts and connectors, clamped the screws in a small vise, heated the nuts with a soldering iron, and applied the contacts with a tweezer. They snapped right into place and the solder fillet wrapped neatly around the entire lug.
The heat from the soldering iron relaxed the insulator sleeves enough to remove nearly all trace of the crimping.
With all that in hand, I ran the brass screws through the case, into the spacer nut+washer combo, through the PCB, and into the battery contact nuts. A bit of tedious pliers work snugged the screws and got everything lined up, then I tightened the spacers against the PCB and battery nuts on the other side. That’s completely invisible inside the case, so there aren’t any pictures, but the idea is that the studs sit flush inside their case recesses and clamping the PCB between the nuts shouldn’t put any stress on the PCB. We shall see.
The slots became so shallow that a screwdriver doesn’t get any traction…