Does anyone know if it would be possible to get a custom 2nd cabinet made in the exact same wood as my amplifier? Preferably Vox/JMI? I know vox makes a handwired cab that is identical in every way, but it just doesn't match.

It has to match that wood.
Look up custom cab builders. It's not gonna be cheap though. The only one I can think of off the top of my head is Bob Burt. IIRC his prices for a 2X12 start around $500 for a pine one. Mahogany is extra. Nobody can put the Vox grill cloth on though.
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As long as you can find someone with wood that has the same grain, I dont see why not.
It'll be hard to find wood to match that mahogany perfectly though, it is natural after all.
Talk to Jesus at AB Custom Audio, I hear he does whatever you want.
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Check out Emperor Cabinets, they could probably do it.
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Didn't they use african mahogany or some super crazy wood for that? i don't think you can get something like that for cheep, check your local lumberyard

African Mahogany isnt hard to find, and its not really expensive either. The hard part will be finding some that matches the grain and colour of the amp.