I didn't know some bands you listed but I took the time to listen to it and I do hear quite some different textures in there so I don't know whether it's possible to cop everything convincingly with a single box.
There's some cranked Marshall type sounds in there but also some more loose and fuzzy or twangy ones.
Some brands you could check out:
AMT, Black Arts Toneworks, Blackout Effectors (Blunderbuss, Mantra), Carl Martin, Catalinbread, Death By Audio (Apocalypse), Dr Scientist (The Elements), Earthquaker Devices, Homebrew Electronics (Big D, Full Metal Jacket), Monte Allums (OD308), Rockbox, Rothwell, Wampler, Weehbo
A RAT is probably one of those drives you can work with and like it or you don't.
For me they never work, I never get enough punch / balls / direct and dynamic sound out of them and I hate that filter knob because it never seems to be right, the gain is also never right, usually it has too much grain and gets too fizzy or too mushy for my tastes but I know other people get great tones with them so it must be me.
Just to complicate things some more, as requested.

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