The Genelex Gold Lion KT77 recommendation is a very good one if you want to explore the EL34 type without the uncertainty and expense of the more sought after NOS tubes.
If you do want to try NOS EL34s a good bet is the East German made RFT. They were branded and sold by lots of companies including Siemens and Telefunken. The supply of them seems to be greater than the exotics and the price lower. As with any vintage tube you'll want to get them from a reputable dealer who can test and match them. Actually, that goes for the KT77s, as well, even though they're current production.
Whether you'd prefer EL34s to your KT66s, though, is a question no one here will be able to answer for you.