I'd also think maybe the driveshaft flex disc is maybe worn out, or maybe the exhaust system is hitting something just in reverse (do to the above mentioned shift in the engine)
As far as the transmission, I believe there is a difference in reverse depending on the position of the "W S" switch by the shifter. Whichever position it's in, try it in the "other" position to see if there is a change.
Gilly

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