The Badlander 100 is actually one of the better Mesa amps I've played in a while - I actually liked it better then the Multi-Watt Dual Recto - if you're leaning Badlander get the 100 and EQ it with your ears. They have a surprising amount of mids already so hate if you will but I dialed the bass...
the only singlecut i've tried that's on par with LP's is Knaggs Eric Steckel model - doesn't feel exactly like the LP but it's very close and they sound fantastic. Agree on the ESP - they look cool but are nothing like a Les Paul.
If I were looking for a LP that didn't break the bank and has none of the coil-tap BS or modern appointments, I'd be all over this:
https://wildwoodguitars.com/product/222230166/custom-color-series-les-paul-standard-50s-figured-top-8/?cat_id=21905