So, I think this would work (although the Sheldon calculator has no 584 
wheel size, I used 27" nominal as option):

24/40 with an (11-13-15-18-21-24-28-34) 8-speed cassette would give me the 
ratios I need. That is like all the ratios of my current middle and outer 
rings combined with similar jumps between cogs.

I could not get wide enough ratios with a 7-speed without huge cog jumps, 
so looks like I would have to use an 8-speed, but allowing good friction 
shifting still.

But that would give me the ratios I need in one big ring, with the 24 as 
the bail out. Though the 6 cog jump to the largest cog looks like it might, 
in practice be too much.

Maybe I just need to stick with the triple. Too much thinking.

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