Tube noise when gain is increased, tube issue?

Finding low noise 6sl7's can be difficult and expensive but that may be the only solution to your problem. What is the sensitivity level of your speakers? If it is too high then perhaps its not so much the tubes as the interface between your amp and speakers.

BTW, what brand of 6sl7's are in your Schiit now?

Most tubes have some noise, some less than others...unless it's humming or buzzing, and does not interfere with the music being played, I'd not worry too much about it.

I have about thirty tubes in my system… no noise… no hiss, no hum or buzzing what so ever.

I have the Freya, no hum or noise at any level. Guessing you have a bad tube. 

The Freya is known for this problem. Do some research and you will find that you are not alone. You might be able to find a better tube but you also might be chasing your tail. I have had 6SN7s prove noisy in Schiit products that are not noisy in all other applications and for this reason I will not retube any Schiit product. I have even hard clients that had Schiit "selected" tubes go noisy in a very short period of time. I had heard that they improved this component in this regard with later production units.

BTW humming and buzzing are not typical indications of a microphonic tube. Ringing and howling are more typical.