UPDATE and Solution (likely temporary)
As many of you have commented, my center stand rested at an angle too far beyond vertical, causing the feet to support only part of the weight while the deployment leg was fully on the ground and supporting much of the weight. Hence the feet had too little friction to activate the leverage of the retraction.
Inspection of my stand showed that the spindle holes were round and had not (yet) worn to a loose oval shape. Looking closely at the surface of the stand where the stop pegs rested, it appeared that portion of the stand had been fabricated at an angle, rather than level/straight, causing the stand legs to go too far forward when deployed.
Before going to the expense and trouble of a permanent fix, I tested my theory with a temporary collar/sleeve fitted to the stop pegs. I worked a 3/8" fuel line over the pegs, and then reinforced it with a brass collar that I cut out of an old brass hose connector. Then I secured them with zip ties.
TA DA! Success!
Now, I will look for the materials to fabricate a permanent collar, probably secured with a set screw, or have some welding done at the pegs or on the angled stand surface.
The pictures with the red tape show the angled surface of the stand where the peg sits, and the peg. The pictures with the hose reinforced by a brass collar show the solution for now.
I doubt that I am the first one to try this, so if this fix exists somewhere else in this forum, I do not intend to hijack it or take any credit. But, it works for now. Thanks to all for your input and help!