Get under there and look at where the driveshaft goes thru a hole before the rear diff. Grab the driveshaft and yank hard. If there is movement, the carrier brating is toast.
I had this issue when I first purchased my car, every shift the driveshaft whould smack the undercarrige of the car like crazy, esp. downshifting.
I'd investigate the flex disk also.
I know that there is a transmission mount but I still have yet to find and replace mine.

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1984 300D