Well assuming Firefox is your default browser, you could try just invoking OSX's open command on the URL. This will work if the browser is open as well as if it's closed.
Open a terminal and run:
open
http://www.slickedit.comIt should open your browser or if it's already open the URL.
So maybe just replace the html-preview command with 'open <url>' rather than have it launch firefox.
Haven't tested any of this, just an idea.
Oh an the open command is at /usr/bin/open, in case it needs a full path (at least on my system), you can run 'which open' from the terminal to find out where yours is, in case it's different (unlikely though).