I would focus my attention elsewhere first...
I've heard of these rubber suspension balls drying out and becoming noisy, and have that in a couple of my machines, but they don't seem to allow the whole mechanism to move more freely, as a properly working snubber should hold down the entire mechanism. If you don't think the machine is too loose or "springy" within the cabinet, I would direct my attention to:
1) Look again at the snubber pad. If it is worn down significantly so that its height has become reduced, the snubber spring may not be able to exert enough force on the pad to properly press it against the snubber plate. When this happens on plastic tub ring machines, the spring itself will often wear gouges on the edge of the tub ring, so you can see when this problem is developing.
2) Check the snubber spring itself. Is it rusting? Is it properly seated in the corner gusset? Are the bolt and nut tight?
3) Look at the snubber plate on the tub ring. Is there a slippery detergent/slime build-up on it?
4) Is the tub ring properly centered, secure and in place?
5) Check the rear leveling legs. The rear legs can slowly sag over time due to breakage or fatigue of two white plastic little clips that hold the leveling link in place. When these clips fail, the steel rear legs will slide too far up into the cabinet, making the entire machine slowly center itself too far back in the cabinet. I didn't know this could happen until I noticed it on two machines of mine and my mother's 1981 Kenmore. This may be why Whirlpool is still making those clips --- people must be buying them. I got some last year that were molded in 2012. If you suspect this may be a problem (look for an uncentered tub ring that seems to center toward the back of the cabinet more than normal) I can help you find the part number for the clips.
6) Check the overall level of the machine, side to side and front to back. Also check the front legs that they aren't loose or not screwed in far enough.
7) Verify the stability of your floor. A weak floor can be a real problem for belt-drive machines due to their weight, especially large capacity models.
8) Is the machine in an overflow pan? This may be a longshot, but when my 1986 70-series belt drive was newly delivered, it was in a galvanized overflow pan that held the machine firmly (it seemed) when not running or when agitating, but when it went into spin the pan would flex as it wasn't perfectly flat, and this allowed the machine to shift slightly during the first few initial spin rotations, just enough to pop off the out of balance relay. Putting it on a secure floor when I moved two years later stopped all that.
Those are the areas where I would focus my attention. When I last checked not long ago, new snubber springs, subber plates, and pads were still available on eBay and from Sears, plus other places as well.
Take some pictures if you're still stumped! Best of luck to you Eugene, we're here to help you.
Gordon
