You can sub a GZ34 (isn't that the stock tube? It certainly was in the original JTM-45) but you MUST rebias. Making this swap will do exactly the opposite of what you're trying to do. The amp will be cleaner with less sag and more headroom.
What you want to use is a 5R4GB rectifier (and rebias for maximum effect). The great thing about these is that they're cheap (about 1/8th the price of a NOS GZ34).