Regarding the rear lower links, there's a possibility of a different problem (from my experience there). I have a rather unique set of custom links now, but even for the stock links the primary source of play of the rear axle was due to the holes in the frame mount wallowing out over time. That is, the 14mm bolt that goes through the links on each end of the bushings for the lower links gets mashed forward and back every time you accelerate and brake. After lots of miles, those round holes gradually become oblong. That allows the bolts and links to slam forward/backward and create play. With more wear, it gets worse.

Unfortunately with the stock bushings, the bushings still have to rotate within the frame mounts so there's a reasonable limit to how tight you can crank them down. I do recommend grease in the contact area at the ends of the bushings. The best solution I have used is to take those M14 bolts into a large hardware store and find the thickest and tightest fitting washers that you can find (either English or Metric washers). Then have a shop weld on those washers on each side of the frame or axle mounts to eliminate the movement of the bolts. You might need new bolts if they show wear as well. (Definitely get grade 10.9 or better of metric bolts if you have to replace them).

All of that may or may not apply to you, but I'm guessing it's the first place to look for play in the rear.

On only one end of my custom lower links I have large heim joints, so I can crank down the bolt really tight and it doesn't affect the rotation of the joint at all. But I still have the stock bushings on the other end.

(I have not had any problems with the upper links and haven't messed with them or the panhard rod).