what are our options. Should the website be completely rebuilt using modern website software? What's available?
Honestly, yes, it should be redone. It may not be fast or easy though... the other option is to keep an old computer with windows 10 to use exclusively for updating the web site.
When I converted mine years ago, I was mostly using FP to add the headers and footers. I used search and replace to convert them to includes. This allowed me to use any HTML editor to edit or create new pages.
I later moved it all into wordpress, which took a lot longer (had over 1000 pages to move) but it gave me the chance to review each page, updating some and deleting others that were way out of date. It's much easier to manage in wordpress. I tested a few other popular website backends but liked wordpress the best. They all had editors built in so I no longer needed an HTML editor.