DefEgge said

When I exit Firefox, restart it, and attempt to save file / page, Firefox offers to save it to a download directory that is different than the one specified under options...

If you enter the directory in Options, Close FF, start FF, is the download dir still there or changed and if changed... to what dir?

~Pj

https://support.mozilla.org/en-US/kb/how-to-fix-preferences-wont-save

Note: Some software, like Advanced SystemCare with Surfing Protection, can protect files in the Firefox profile folder against changes. If you have such software then check the settings or uninstall this software.

Are you using any download add-ons?

Sorry, I have been away for a bit and am just seeing the replies. Thank you for the suggestions.

Pj, no the download directory is always reported correctly and I have never seen it change (even upon confirming that it is properly set after the wrong directory is used or offered).

Fred McD, the support article that you linked was one of the first that I consulted. Options therein did not correct the problem.

No download add-ons are installed.

I will need to double-check that the problem persists after the add-ons (NoScript, Privacy Badger, uBlock Origin, Tab Counter, and Zotero Connector) are disabled. I am fairly certain that I had previously check this but I do not see any mention of the test in my notes.

I have checked - just curiosity - to see if the windows registry showed any mention of the aberrant download directory.

If all else fails, I will try uninstalling, deleting the profile, and reinstalling.