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Thanks for the suggestions guys. I don't think either of those modules does what I'm looking for.

The Time Wizard does look very cool and is clearly overkill fro what I want. Having peered through the manual I don't see a straight forward way to even get the binary divisions I want. The switchable ratios are 1:1, 1:3, and 1:4. If that 3 was a 2 it would basically work, although it seems ridiculous to use such a large and powerful module for such a small task.

The Fractio Solum looks good also, but I want to be able to instantly change the ratio, which I doubt I can do with an encoder.

I expect that this would be easy to DIY, but otherwise it looks like basic clock divider + switch is the way to go.