David, in most modern high gain amps, a more substantial percentage of the tone comes from the preamp section, not the power section of the amp, unless you're truly cranking it. Your original post doesn't mention whether you're after recommendations on preamp tubes, or power amp tubes.
Also, there really aren't "high gain" tubes, per se. There are tubes, and the circuits are designed to push them into higher gain levels, and often the gain is cascading gain from several gain stages.
Therefore, the circuit itself may work really well with some tubes, and yet a different amp may not make those very same tubes sound the best.
You may be aware of this, of course. Some companies (JJ comes to mind) make a hotter preamp tube than most. So that may tend to break up nicely. Or...not.
On the other hand, you may or may not care for the tone to start with. All of this tube stuff is so personal!
The most balanced sounding EL34 power tubes I've found (other than ultra-rare and expensive NOS Mullards) are German-made NOS Siemens, but I'm not a high gain player so please take that into account in deciding whether they'd be for you. I crank my amp that uses them pretty loudly (PRS HXDA), but keep in mind it's a vintage type of amp, and they might sound radically different in an amp made for the preamp tubes to handle most of the gain action.
I'll also put in an argument that NOS Mullard preamp tubes (not the new ones made in Russia, the old ones made in the UK Blackburn factory) are richer sounding than anything new out there, smoother and fatter to boot. But they're expensive, when you can even find them. I keep one or two sets of spares on hand, so I tend to stock up on the NOS stuff and have it ready just in case because of the difficulty in acquiring them.
There is a certain amount of insanity, if not wishful thinking, that goes into this tube rolling stuff, but for the most part I do find that the NOS tubes made in the 50-70s are more reliable and that they perform better. In a way, I'm kind of amazed that after 40-60 years, the darn things are even available at all!