"For something that only needs a small number of fixed positions (up to about 16 or so), a Geneva is FAR simpler........"
...could be true, but this is only 1 position. 1 complete revolution.
With the Geneva, you'd need the aforementioned gearmotor including a drive for it, the Geneva mechanism with whatever indexes you might choose (say 4) then a timing belt (or chain) geared 4:1 , mounting and machine work to set it up ........
I'd still prefer the indexing drive and stepper motor directly coupled to the feed worm shaft.
Software is free, VERY small single incremental move to program (infinitely adjustable for acc, dec and speed) just a few wires to hook up.
Would be much simpler imo.
Russ