no need to change the transfomer? or even the tube socket?
you may want to research the internet..
the KT66/6L6GC, the EL34 and the KT77, KT88/6550 all share the same socket pinouts, so plug-in and bias is possible...
in fact, a lot of other tv vertical output tubes such as the 6V6, 6W6, 6EZ5 etc. share the same socket configuration...
the thing is, it is not the tubes per se but the output transformers that define the character of your tube amp,
so no matter what you do with the tubes, if your OPT is not up to it,
then you may not get more mileage...
here are two scenarios....
1. replacing your EL34 with KT88/6550 will let you bias it to say 60mA per tube,
the B+ will drop further than say 400, power will most likely stay the same,
but distortion characteristics will surely change...
2. replacing your EL34 with KT66/6L6GC, B+ will most likely be higher than 400v,
bias is at 30mA, again power stays the same and distortion characteristics change...
which one you will like remains to be seen...