Now that you mention it, Dolly and other Rainbow Bridge tunes were done with Mitchell, weren't they?
Yes, Dolly was was done with Mitch but not certain about "rainbow bridge". The only thing Buddy added was the fact that he beat the drums so hard that they actually sounded like a damn machine gun in the song machine gun. But that's about it.
I play a 68' Les Paul special - for that gruff zepellin/Mayall blues sound, and I also play a 59' American Strat (much like SRV's number 1 - I had it customized to match his set up) for that plink plunk Hendrix, SRV, clapton sound. I play in the E and A chord families most of the time (old blues men never play outside).
Go listen to the band of gypsies, live at the fillmore east. It sucked ass. Compare to Isle of wWight or Woodstock or Berkelley performances, and then you tell me whick three piece was the best set up for Jimi's sound and energy.