Just to follow up on this one, I picked up a couple dozen Easton 3D Supernocks. They definitely have a much softer snap onto the string. The nocks I had acted more like "jaws" on the string whereas the supernocks have a profile that just seems to "wedge" the string snugly between the two flared ends.
They still take a bit of pressure to pull from the string, but not quite as much as the old ones. They certainly don't fall from the string with a light bump.
The last thing I may try is to find a piece of metal rod or similar approximately the size of the served string or slightly bigger. Then place the nocks on it, steam or heat them, and leave them for a few days to see if the shape changes to a slightly more open profile.
Thanks for the suggestions.