*sigh* Ok, finally.
Here's what I've found out, and it seems like this will fix my problem with file uploading in Flex/Coldfusion.
Firefox apparently uses two windows when dealing with file uploads as pertains to Flex.
What happens is, that second window drops the session info, and you wind up getting a 302 httpstatus code. (as a note, using something like Ngrep in linux or Windows, or Wireshark in Windows, to sniff your own network traffic to see the raw response will help you decipher what's failing. I was able to see that it was trying to redirect me to the login.cfm template)
What fixed it was returning the JSESSIONID from a Remote Object/CFC call, and using it in the URL string that I used in the URLRequest upon file uploading.
I.e., var req:URLRequest = new URLRequest();
req.url = "upload.cfm?jsessionid=" + jsessionid;
req.method = URLRequestMethod.POST;
fileRef.upload(req);

"JSESSIONID" is set a little above the code with the Remote Object/CFC call.
And voila! That's how you upload files if you're behind HTTPS. *whew*