Following Dylan's lead, here's the recipe:

Preparation time: 5 minutes, plus printer time (an hour each in my case)

Ingredients:
1x Threaded rod: Material, size, pitch and length to taste.
1x Nut for threaded rod
1x Cup magnet with mounting hole, size to taste
1x 3D printed base
1x 3D printed nut holder

Step 1:  Print the base part

Step 2: Print the nut holder part

Step 3: Insert the threaded rod into the base

Step 4: Screw the magnet onto the base

Step 5: Insert the nut into the nut holder

Step 6: Spin the nut+holder onto the threaded rod

Done!  

I got the cup magnets off Amazon (arrived in 12 hours): cat number B09ZX7SXMF "MAGXCENE Strong Magnets with Holes"  in 16 mm size.

The printed parts are modeled in Fusion 360, and printed in PLA.  I used a 0.3 mm nozzle and 0.1 mm layers.  It's helpful to chase the threads with a tap (1/4-20 in my case), and ream the hole for the magnet screw to size with a twist drill (2mm or 3/32 work for the mystery screws I got with the magnets).

They work splendidly, though they do grab the plate a lot more aggressively than the ceramic magnets I used in the previous iteration, and I'll have to get used to that.