A bit of rummaging produced a desk lamp arm, minus whatever lamp it originally held, ready to hold the second photo lamp, after a bit of epoxy on one locking knob:
The flanged nut will seat on the wrecked part of the knob, with the epoxy holding it in place and somewhat reinforcing the perimeter. I’m not sure this will last forever, but it’ll be a start.
Printing a second cold shoe, though, worked perfectly, and everything fit:
I love it when a plan comes together!