I was wonder in terms of the difference between simply tying the legs together, as with an A-Frame, and the fact that with a spider, you are perhaps introducing an additional 'sprung system' between piano and floor.
Each of the three arms of the spider pivots on fulcrum created by the wheel, the downward pressure of the piano leg beyond the wheel tending to push the arm up, and the central plate needing to be very secure in order to resist the upward pressure.....
No worries ... it's strong enough to bear the stresses you identify. But it does serve as a mass-loaded cantilevered damper to effectively isolate the sound traveling down the legs from the stage. A piano standing on its own casters has a greater presence than one on a spider trolley. I would wonder if the A-frame might be a bit between the two.
There are also playing differences, as well. Our PTG chapter conducted tests with a Baldwin SD-10 mounted on a spider trolley on a wooden stage both with and without screw-jacks under each arm at the leg locations. Seven of the eight people there could hear tonal differences with and without the direct connection to the floor. At least some of those who actually played the instrument both ways also noticed a greater sense of precision with the jacks in place.
The ideal (if one wants to spend the money) is to use a transporter
and leave the piano on its own wheels onstage.