Just a follow-up. Cory emailed me a new license key (thanks, Cory!) and I was able to install the 2017-18 version. I had a hard drive failure in the mean time and installed on my new solid-state drive... which, by the way, is blazing fast.
I never did hear back from SolidWorks support after the initial "We have received your email and will respond soon) back on 11/11. I know their emails make it to me, because I received the confirmation of my inquiry - plus I run my own mail server, and see all the logs of email that gets rejected. The emails I did receive from SW never contained a new license key, always the old one which didn't work.
So, I'm supposedly good until next December, when I hope the renewal/re-installation goes smoother. Cory, thanks again for helping to get this sorted out.
Dale