I fully agree with John's diagnosis. The ability of the driveshaft to shorten/lentgthen through the spline connection is normal and necessary.

A somewhat similar experience occured to one of my 544's years ago, the car started making an awful noise upon accelleration, in the beginning only in left turns but thereafter always. The problem was found to be worn out engine mounts, as the exhaust pipe near the manifoil would touch the bare steel due to flexible engine sideways.

Rubber will always wear out after some years, even if it's a Volvo...

I had this problem on my PV544 many years ago. There are four rubber blocks which prevent the axle from twisting. One pair of the blocks prevents the axle from twisting under acceleration, and one set prevents the axle from twisting while braking. The blocks wear out internally, and you must remove them to see the wear. The pair of rubber blocks which prevent the axle from twisting under acceleration on your car are worn out. Order at least two of the blocks before taking the car apart. If the blocks aren't too expensive, order all four.

I bought my PV 544 in 1968, and sold it in 1972. The problem occured 1969-1971. The original blocks only lasted about ten years. Your car is well overdue.