Media Uploader Fails to Upload

Both the multifile and browser uploader are not working on my site.
The uploader creates a record and link for the image, but the link is broken, and no new directory is created in the uploads folder for this month. (I am testing with a small JPEG.)

The media library will show the record, with a broken image symbol, and the link leads to 404.

My site:

https://www.webpeoplemedia.com

I am running:

WP 4.1.1 with Atahualpa 3.7.13 theme.
PHP 5.4 (Single php.ini configured for max upload of 200MB).
Dedicated IP with entire domain under SSL, on Bluehost shared.

I recently added a plugin called ShortPixel, which works within the media uploader to compress images and save backups of the originals. There was a bug and an update. When I found the upload problem, I deactivated, and then completely deleted the plugin, in efforts to fix the issue, but the issue remains, and I cannot be certain it was caused by this plugin because I had not tried to upload an image since early February (before the 4.1.1 release of WP) until yesterday. So I suspect the plugin, but it’s gone, and still my uploader is hosed.

In addition to removing the above plugin, I have tried:

Deactivating every plugin on the site.
Upgrading my PHP version and checking the PHP.ini file for errors.
Reinstalling WP web root, admin, and includes from a fresh download.
Reinstalling .htaccess.
Removing depricated WP files from web root.
Renaming an old wp-config file in an old install (from before I changed my primary domain and went to https).
Checking site settings for errors or inconsistencies.
Checking various error logs.
Setting file permissions for uploads and all of its subdirectories to 777 (I have since set them back to 755).
Uploading from a different browser, or uploading a different image.
Throwing a virgin into a volcano (jk).

Help? And thank you in advance. 🙂