Stanner is dead right. It's like setting two friends up and they fall in love and never part. But an amp and a pedal. So yeah, best friends.
I have a 1st Gen Model T, with an 80's Small Box Rat, all through a late 70's Marshall 1960B cab (w/ a set of really nice G12T75s), and I've never had any issue with the harsh brightness (that sounds so goth). The speakers are a bit brighter than I was used to (having played through Sunn 612S cabs previously that were beautiful, but back-breaking), but definitely not harsh.
I've had Tung Sols, EHX, and Svetlana tubes in both the Ts I had over time, and yeah, never a problem.
I'm big on diming mids, bass, and rolling off the treble and the bright gain knobs a bit. You've got a 2nd Gen, so maybe work that mid-switch.
Maybe consider your pickups, as well? I have a Gibson Sonex with some pretty obnoxious pickups, and I get the least rad feedback from them. Speaking of which, anyone want to buy a Lefty Sonex?