Hi Russell,
I think that the spider dollies don't make a difference for this problem. Seems to me like the biggest issue contributing might be dryness in the winter that might make the fit of plates, screws, or glues joints loosen. Also train the movers! The piano should in my opinion always be moved in the direction of the round end-round end/single leg end first. When the piano is not on the spider dolly it is easier to feel the sloppiness of to the top of the leg to the bottom of the leg glue joint if it is loose. I make sure that I check this feel of the legs each time I service, but I don't usually look of the wedged or cams unless there is a dry snap. All of my school's pianos are newer now, so they have the new plates and Allen bolts.
I have two jack in the boxes and the school owns a grand transporter. I would use the jack in the box to raise the piano to feel the leg if I was unsure of the fit. This is the only way to be sure if there is something going on. With no weight on the leg you can find a problem. My guess is that when the piano is moved over a threshold they aren't trying to take some weight off of it. In the past I have had the taper wedge come loose from dryness on many pianos. The cams turn or be loose and the leg post glue joint fail. The piano should be raised to reset the leg and turn the cam in to a locked position and tighten the screw.
Using the jack in the box. Cut extra blocks of 2x4 and 3/4" stock. You need these to go under the cup ends of a spider dolly and on the new S&S style legs, the plates are so thick you'll need to raise the bottom of the jack in the box. I never leave a piano on the hydraulic jacks alone. I slip blocks in between the top of the jack in the box and the piano in case the hydraulics fa,,l the piano will rest on the box.
It is also possible that your wheels need a clean out. Yuk there is always hair caught up in wheels.
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Jessica Masse RPT
Western Michigan University
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