A Hagstrom Swede or Superswede can sometimes be got in the USA at a decent price (originals, not the current re-issues) and contrary to what is said above Zappa not only played one but also endorsed them. Out-LesPauls the LesPauls.

If however you are after the finesse of a palette knife rather than the power of a sledgehammer, try a Parker Fly. Look funny, sound wonderful.