The hum sounds like a grounding issue, but troubleshooting that can be "fun". As to imbalance - this can often be due to the tube used, though djusting the trimpots may or may not help. This is where it helps to have multiple tubes to play with - the odds of two tubes being identically imbalanced are relatively slim.
What kind of power supply are you using, and what's the output voltage? I've had some horrible problems with noise and hum with non-isolated supplies. I eventually settled on one of those 24V Meanwell SMPSes that are like $15, crammed into a plastic enclosure. Dead silent, which surprised me greatly.
I'm not sure where you're at, but if you're really extremely desperate for cheap tubes to play around with in this, I've got and am happy to part with a new 6N23P that's only been used for an hour or so. Really very nice-sounding, just very very microphonic, which is subpar on a desk with two computers, in a house with four people and three cats.
I've also got a 1979-vintage Chinese military 6N11, that was "OEM" with one of those cheap Bravo Audio amps, which I'd be happy to get rid of. Don't really recall anything about it, to be honest. Probably not as good as the Electro-Harmonix 6922s, but probably better than the current-production 6N11s.
There are some probably-quite-decent 6DJ8s and subs on eBay right now, quite cheap - including some 6N23Ps at a bargain price that are probably worth pouncing on. Otherwise if you hunt around a bit, you can usually come across NOS JAN 6922s for reasonable amounts, and all the ones I've tried (Phillips/Sylvania) have been extremely good. Ditto the Electro-Harmonix 6922, at least in the cheaper, non-gold-plated version.