Refining a Sublime Text 2 / Transmit workflow
Answering my own question here.

A follower on Twitter recommended Sublime FTP ($16), a third-party add-on by the author of Package Control, Will Bond. 

For my own setup, I use his Sublime SFTP Solution which maps a local folder to the remote version. This setup allows me to quickly access my files.

Since working with remote files can come with some risk, I use Joel Thornton's Automatic Backups add-on to create a time-stamped backup of whatever file I have just saved. That way, in case something tragic happens, I can quickly roll back to an earlier version of my file.