Hey Max! I remember you from Elite Syncopations! It's nice to see you're still composing!
Anyway, I agree that this piece would lose its ability to fall under the hands if transposed. Nonetheless, it would be easier to read in F-sharp and B. That would get rid of the E-double flat chord in the opening (changing it to D-natural). As for the double-sharps that would occur, they are more efficient than double flats. They have their own symbol, distinct from two sharp signs.
Anyway, it's a great piece that James Scott would no doubt have been glad to have composed!
SAS