The guitar could be the problem. He was playing mostly Les Pauls and 335s during that period. That is if you are talking about the original recording. As far as the amp choice he was still very in to Marshalls around that time. He didn't really become a strat enthusiast until around the time that The Band did their farewell concert. Word is he became very impressed with the strat guitar and shorter more meaningful songs and solos after doing that show. Boy, do I feel old now!
Don't forget George Harrison's guitar track on that song. He was discovering the guitar/leslie cabinet combination. I don't know exactly what Harrison played thru in to the leslie. I do know Clapton pushes his leslie with a Marshall head.
While I like the TH2 amp a lot, I find myself using some stomps and the Brunetti amps most. There is a nice choice in the Lynch Box head as well. The Randall is very good for heavier stuff.
I am still playing around with the TH2 default amplifier. I just haven't found anything that has made it in to a project yet from that one. The one amp in there I really like is the Tumble OD. No, it's not a Dumble but it is pretty flexible. Lots of tone.