With EC_Joe's help, we resolved an issue introduced by 5.7.4+'s implementation of proper URL structuring, so I thought I might post it here in the hope that anyone else experiencing a similar problem may be helped. The issue presented initially when updating from 5.7.3.1 to 5.7.4+ appeared successful, but forms were nonfunctional as described below. The problem here is that previously introduced url rewrites called from .htaccess for implementing canonical urls (to force prepending of www to domain and/or to force https SSL) are now redudant due to the new link structuring, and are causing form tokens to be lost in perpetual redirections.

The symptoms:
* Unable to clear cache
* Unable to save changed cache settings
* Submit buttons do not work
* Exception thrown when users attempt to submit form on frontend
* Attempting to log back in after logging in results in "Invalid Token Error."

The solution:
1. Revert to pre-borked state with site and database backup.
2. Clear browser cache.
3. Remove/comment out any URL rewrites from .htaccess.
4. Login as admin.
5. Update to 5.7.4+ through your method of choice.
6. Reintroduce https and/or canonical redirects through dashboard under "URLs and Redirection".

Hope this helps someone else, and thanks to EC_Joe for assisting in running this problem down.