You have the right guitar at least! Joe typically does not use amps with EL84s in them and is more of a EL34/6L6 guy. Do not fear though, because there are some great pedals out that can get you in the ballpark.
Some of the pedals that other people here have had a lot of luck with are:
Fulltone Fulldrive 2, Fulltone OCD, Ocean EFX Texas Deuce, Ocean EFX Pearl Drive, Ibanez TS9 or TS808, Fuchs Plush Drive, Fuchs Creme Overdrive, Xotic Effects AC Booster+, BB Booster +, BB preamp, Carl Martin Hot Drive & Boost, ect.
The trick for that big fat overdrive sound is achieving just the right amount of compression and sustain but still maintaining the string clarity/dynamics. You don't want to have too much gain because then it just sounds like mush. With that particular song it's more of Joe's "rude" Marshall sound so pedals that are in the Marshall vein may be better choices. Emphasize the midrange and keep the treble down a little. Joe's sound is not piercing but instead a throaty, midrangy sound. Good luck!
'67 and '74 Fender Twin Reverbs, '74 Marshall 1987 lead mkII, Metro Superlead 100. Pedals from TC Electronic, Ibanez, Dunlop, BK Butler, Electro-Harmonix, Fulltone, Maestro/Gibson, Loopmaster switching, VoodooLab, Boss. Gibson and Fender guitars, Dimarzio pickups.