just because the EL34s look physically different, doesn't mean they aren't matched in terms of current draw. However, if you want to pop some new EL34s in there, go for some Winged=C= ones. If you have a bit more money to spend, get some NOS Mullards, brown-base Teslas or Siemens.
if the top end is a bit harsh, you might also try some 6L6s in there (depending on the plate voltage), but that will require a small tweak of the bias circuit.
the main reason that the Selmer T&B amps are quite bright is that the presence is hard-wired on full. a reasonably competent tech could tweak this for you, or even install a presence pot on the back of the amp in place of one of the speaker output jacks. I think this will give you what you're looking for from the Selmer - I've owned loads of them over the years and used to gig a pair of mkII heads.
where are you based?