Ok so I dug up the error logs, kept seeing “Option ExecCGI not allowed here”, and did some googling about what it is.
Turns out, it was not related to the image compression process after all, but rather a nasty after-effect from a security plugin (Wordfence) that I had already deleted. Fixed it by deleting the additions that Wordfence had added to the .htaccess file under the uploads folder. (Somehow I didn’t think of checking those elsewhere before, other than the root…)
Sorry for the trouble, everything is working smooth as butter again. Just leaving the solution here for anyone else possibly having the same issue.