It sounds like you have a good handle on the situation.
It also sounds like you have plenty of gain to spare. Reducing that gain will actually improve the S/N ratio of your system and should make it sound better as a result. So the transformer idea is not a bad one.
Since you likely have caps in the output of your tube preamp, I'd recommend a parafeed output transformer, like B7s from Magnequest (about $60/ea). I'd wire them up into a pair of IC's. Put it close to the preamp end. Then you can actually experiment with and without. If you really like the result then you can permanently wire it into the preamp.
A note about picking the right B7, since you have choices. The B7s are quoted in impedances. You most likely want the 5K:500. 5,000:500 is 10:1 impedance ratio, but turns ratio is the square root of this, or ~3.2:1, so voltage gets stepped down 3.2 and current gets multipled by 3.2. The Zout is 1/10th the original though. The 10K:500 is roughly 4.5:1 voltage ratio, 20:1 impedance ratio, but I recommend the 5K:500.
Said another way, if the load you are driving is 12K, if you are using a 5K:500 impedance ratio, then the preamp now sees a 120K load instead of the 12K load. Transformers are cool huh?