$500 is a bit tight...while not super quality, a Cort Curbow is only a little longer than a short scale bass yet, it is 34"scale, has 26 frets on the E and A strings, 24 on the D and G. This is due to the really small body on the Curbow, not sure what the string spacing is for a 5 string or 6 string as I have a 4 string - but they looks to be narrow, perhaps similar to the Ibanez. No measurements available as the Curbow is no longer listed on the Cort site but you can probably find one online used.
I'm posting this picture from another TBer Kodiakblair - the Curbow is in the middle. To the right is an Ibanez Mikro which is 28.6" scale.
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Since I have a 5-string Curbow (version 1, but version 2 is only electronically different AFAIK), I just measured it. 17mm at the bridge, 9 at the nut.
They detune quite well if you use suitable strings. I don't think I'd like the tone of a fretted Curbow, but the fretless is quite nice.
Or, if you have the budget for a non-temporary bass... something about the geometry of Dingwall basses makes them very easy to pick despite the 18mm spacing. So if you can find an NG2 or ABZ, that would almost certainly be a keeper anyway, and Sheldon Dingwall is pretty much the king of down-tuning. But not going to be $500, think more like $2200.