Thanks for the advice, all.
T-Mar, I like your suggestion, especially given the apparent limited availability of uniglide cassettes. One of the things I like about the 6 spd 105 is that its just about equally nice to use in index or friction mode, so running a 7 speed cassette in friction would be no big sacrifice.
Would a 7 speed freehub body along the lines of this one would fit the bill?:
https://www.treefortbikes.com/Shimano-RM30-7-Speed-Freehub-Body?utm_source=google&utm_medium=cpc&adpos=1o2&scid=scplp333222399936&sc_intid=333222399936&gclid=E AIaIQobChMI9dHJoe-63QIVhoTICh2egwiaEAQYAiABEgKCVPD_BwE