Yeah I would be surprised if the Piledriver didn't do well with Alpinist and Fall of Efrafa type material.
There are definitely clips of it in Drop C online, not your style of music so the EQ on the amp is most likely set differently but you'd get the idea. I'll see if I can fine one and post it
Tim from Tombsealer used a Tele, as far as I know it was just a Fender USA Standard, no Quarter Pound in it or anything. He did have Izzy backing him on rhythm guitar with EMGs though. They are at least as heavy as Amenra
Bert from my old d-beat crust band Terania uses a MIJ toploader Tele with a SD Quarter Pound in it, that has a lot of output, possibly more than you want. I wired it straight to jack and he stopped using an overdrive. He only uses overdrive when using his P-90 equipped Epiphone SG now, the Tele doesn't need it. He is the guy who introduced me to Alpinist and Fall of Efrafa, he's right into that kind of sound.
EDIT:
These are the demos of the Telecaster with the Piledriver set in Drop C.
https://www.youtube.com/watch?v=3GkBLyIzKjs (Peavey 6505+ 112)
https://www.youtube.com/watch?v=fJPpPj40UIA (ENGL Thunder 50)