The "'Burst killer" moniker is traditionally reserved for "first-rack" ES345s from 1959...but indeed, just about any ES335, ES345, or ES355 are extraordinarily versatile instruments.The ES-345 works for me! "The Burst Killer" as they are called.
My ES-335 is my Cold Dead Hands guitar.
I even had a truss rod cover engraved to that effect.
It’s a run-of-the-mill 2002 Dot Reissue in Cherry red transparent.
Bought it new.
A couple of years ago, I added a Bigsby via the Towner adapter kit.
Until then, the only mods I had ever even considered were the Schaller straplock pins.
Only thing I could imagine that would be better is possibly an old school ES-330 set up the same way.