Well, as usual, y'all have helped steer me in the right direction.
While I had checked the root .htaccess file, I later discovered a rogue .htaccess file inside /wp-content that was causing the problem. It was created and left behind by a security plugin I tested (and deactivated) a while back that, wait for it...prohibited execution of .php files where they aren't expected – like the SP CSS.
So technically, this was never an issue of CloudFlare not playing nice after all, at least not yet. Still testing that theory. Now that I have the stylesheet issue resolved, I can get back to testing.
Thanks again for the excellent support!
Simple:Press powers the Tripawds Discussion Forums.
It's better to hop on three legs than to limp on four.
The Tripawds Blogs Community is made possible by The Tripawds Foundation.