I agree with HJM that a bit more drive than a Mule would be good, though I like Ratrod's Riff Raff suggestion -- or maybe even an Emerald?
Back in the day with M'head, Fast Eddie played a strat, as much to cut through the mix as anything else, I think! So, anyway, for a mahogany body like the Epiphone, you'd surely want something with plenty of bite in the midrange.
And, hmm, given that Brian Robertson played a Gibson when he was in Motorhead, maybe an Emerald would be appropriate! :) (I can see why he didn't last in the band, but I think there's some great and often-overlooked stuff on the Another Perfect Day album.)