Here's what I wound up doing to solve the problem:
- Created a folder for my faxes: ~/Faxes
- Control-clicked on the folder to enable folder actions as explained here.
- Saved this script in ~/Library » Scripts » Folder Actions. This is a script that I modified from the OS X folder action script named Image - Duplicate as JPEG.scpt, which you can find on your Mac in the /Library » Scripts » Folder Action Scripts folder.
- Attached the above script to the folder using the above instructions.
- Saved this script in ~/Library » Scripts » Applications » Mail. This is the script that I modified from this source.
- In Apple's Mail, I created a rule, set to "All conditions met," with these criteria:
- Any Attachment Name - Contains - .pdf
- Account - myfaxaccount@faxaddress.com
- Run Applescript - pointing to the script saved in the previous step
[robg adds: I haven't tested this one. The information above was taken from the linked blog post, though I have reformatted and rewritten pieces of it for easier reading here.]

