Sturmer Archer sprockets for geared hubs are not compatible with the usual ("regular" matches my understanding) threaded flip/flop or double fixed hubs. FWIW I fitted a 22t (biggest that would fit in the chainguard) sprocket to youngest daughter's Shimano 8-speed hub (caution... that was 6 years ago). It seems odd, but I'm sure that those components were 3/32", rather than the traditional 1/8" chain width for fixed gear & single-speed transmissions (I use 3/32", but that's not normal). It's possible that you're referring to freewheels that would fit on a threaded hub. I think that's unlikely, but ICBW.
I've tried to find threaded cogs with more than 22 teeth in the days when Will was still running HubJub. By now, I can't remember who made the 23t, probabaly E.I.A. or Andel. However Will seemed unable to obtain them (on reflection, he might have been able to, but not on terms which would have kept his business solvent). I'm not up to date with
Hubjub's offerings (E.A.I. are no longer supplied in 3/32" width), but 22t seems the limit.
Meanwhile I'm untroubled by the fuss about co-prime rear cog & chanring teeth. I ride 50x20 & have yet to observe any wear patterns corresponding to that simple 2½ ratio, though I do rotate the chainring when I renew the chain. Also at 73 I'm a long way past it.