I had a wonderful long message typed up, but then the authentication broke, and it dumped my message. So, here's the short and skinny:
* it was texlive causing the issues
* CentOS includes a version of texlive that's snap-shotted, not particularly good, and doesn't support the full TUG list of packages
* this was causing pdflatex to fail because it couldn't find the path package
* manually install texlive-2017
* change all user paths to point to these binaries instead of the yum installed ones (because if you uninstall the yum one, it also deletes R from the system, which I need)
* go into WW configuration (site.conf), and point directly to the three binaries needed (pdflatex, latex and dvipng)
And it works! Not flawlessly, but it's just minor stuff at this point.
I will try to update the wiki on these issues to bring Arnie's suggestion of testing the check_latex.tex file before anything else. I did install WW with the usual script, and it seemed to complete fine, but I must have missed something failing in there. If I get a chance, I'll try a fresh install onto a fresh CentOS VM and see what happens if texlive-2017 (with path) isn't installed. It'd be good to be able to warn people in advance.
Thanks again for all of the help, this issue is sorted.