There is. In power tubes and in power amp topology. I just tested a whole bunch of different tubes in my RM100 and also compared RM100 power amp and Fireball 100 power amp with the exact same set of tubes. The Engl has a lower reaching low end, without having measured it, feels like the RM100...
BEBB, IICP, Ecstasy, Pittbull, Powerball, DS and as of late BE DLX. BMAN for vintage tones. Deliverance also but the clean is very light on low end and my least favorite.
High pitch squeal could also be impedance and or ground related, had that problem 1 week ago in my own rig. I don't understand why, but a buffer before my loop switcher solved it in the test rig and a buffer plus iso transformer did it in the big rig.
To help you find the issue I'd need more info on the exact signal chain. Guitar > Redeye DI > Amp In? What else is connected to the amp?
And how exactly is the DI connected? What cables what in Out goes where?
What interface?
I have the same DI in my setup and guess we can find a solution :)...