Do you hear that same noise when just playing acoustically?
Not at all acoustically.
It's very very faint with the Slinky's gone and replaced. I have to really listen for it. My wife could not hear it at all. Certainly playing along with a CD or a band it would be completely lost in the mix.
I will probably never know for sure, but the 5879's if you tap them are more microphonic than typical 12AX7's. I'm thinking something about that tube with the brightness/boing of the Slinky's just wouldn't work?