Thanks, Bingen. I just got off the phone with Adam at NetApp support. He and I verified that we can't delete the vVol with the usual commands provided by the VSC plugin and that we'll have to use some combination of ONTAP System Manager, vCenter, and the Web based CLI interface [sic.] at https://ww.xx.yy.zz:9083/ . He's going to test this out and send me a list of tasks to do. I supplied all requested logs with my original ticket (2008782637) in case anyone at NetApp wants to look at them. My main focus now is just removing the broken vVol.
Most interesting is that there is a new 9.8 version of the VSC (with a totally different name) that's been out since *February*. I didn't know about it since the product's name had been changed and there was no mention of this in the old download location. For anyone who wants to upgrade, the product is now called "ONTAP tools for VMware vSphere," so go to NetApp Downloads section and you'll find it under the letter "O."
Given that I was running the latest/last version of the "old" software, 9.7.1P1, and would have never known there was anything newer, I would recommend that NetApp add some kind of link to the new version/newly-named software from the old location. (Especially since this last version of the old software was what I was running when my vVol broke and others may think 9.7.1P1 is the latest and greatest...)