Thanks again to all for input and replies.
And thanks to Dave S for recommending the frame-specific kickstand plates. Got a pair, they work great. Part of the trouble with the existing plate (installed by previous owner or their mechanic) is that it was a modified Pletscher plate. Had to be modified to clear the chainrings.
I removed the stand because it was super stiff and it wasn't closing. I dry brushed it and then blasted it with penetrating oil, which is disgusting. I then cleaned it as well as I could with several passes with brushes, rags and compressed air. Then appleid some Boeshield.
I touched up the frame damage shown in the original post by lightly sanding and then applied some Testors. I wrapped some Newbaums on the stays and carefully re-installed the kickstand. It works like a new kickstand with lots of snap and a feather touch to open and close.