Jan 17 2016
So basically, set up $wgCacheDirectory to a folder writable by MediaWiki. That, of course, is not an option during the installer.
I can change open_basedir during installation and then use this afterwards. This is a good solution I can live with.
Jan 15 2016
The solution is the add /tmp to the open_basedir. As I am going to be deploying to a shared hosting environment, I would strongly prefer NOT to do that long-term. Any chance I can designate a different location for the temp directory?
Sorry for the delay in replying. I had reverted back to a previous version to avoid the bug and had to re-install to try things out.
Dec 19 2015
There are open_basedir restrictions in place, but the root of the wikimedia install is included. Which other restrictions would you like me to check?
Dec 1 2015
That was the error I received before setting $wgTmpDirectory. Afterwards, it changed to
Less_Exception_Parser: Less.php cache directory couldn't be created: /home/thegymnc/wm_tmp in ..../vendor/oyejorge/less.php/lib/Less/Parser.php:441
which is the directory I created for it.
Following the next bit of advice in the thread, I looked at URLs containing "only=styles" and did see errors.
As suggested by the Support Desk thread, I looked at https://www.mediawiki.org/wiki/Manual:Errors_and_symptoms#The_wiki_appears_without_styles_applied_and_images_are_missing.
Everything mentioned checks out as correct.
It looks like it or a similar problem has been posted there since I posted this. They don't seem to have made it very far in regards to identifying what's wrong.