So, another possibility, is get regular sturmey cogs ground thinner, to take 3/32 chain, as they make 1/8" thick to 22t.

Highpath Engineering, In Wales UK, has made some larger cogs of aluminum to fit in these situations , before , [seen pictures] and as they are set up to make custom chainrings for any user, they may do so again.

Ive been pretty happy with My Mountain drive kit, a 13/15 set on the hub would narrow the spacing and double the ratios.
so there would be 12 vs the nicely practical 6 , there is no overlap of any ratios, the 3<>4 gap is only slightly wider than the 1,2,3 at 33%, its 41% as i recall .. on Sheldon's Gears calculator site ..