Pictures would help (particularly around the connections to the tube sockets), but it sounds like a combination of things. There could be some grounding issues and any competent tube tech should be able to fix those. Additionally, the tubes could be oscillating due to poor construction. Oscillation can manifest itself in a lot of different ways, from static, to hash, to squealing, to microphonics, to ringing. 6sn7's are not known for a propensity to oscillate, but any tube can, given the right (or wrong) environment. Really, you'll need a scope to know if this is the case, but if there aren't measures to quell oscillation taken, then adding them is as good a test as any. This means adding grid stopers, and in extreme situations not likely here, plate and catjode stoppers as well. The tubes could also be picking up interference of some sort which would be cured with some shielding.
As a first go, try making shields out of aluminum foil and wrapping them around the tubes. Literally, this means wrapping a tube of aluminum foil around the tubes. Be sure they are grounded to the chassis -- probably touching the screw that holds the socket on will be good.
edit: ah, you are using those dumb tube adapters? Almost certainly oscillation. Could be other stuff, too, but those were a bad idea from day 1.