I had a hiccup pressing a button once. Was kicked back to initial screen and the student was "locked" - which requires an admin to reset.

So: maybe, but the back end is probably too flakey. Official recommendation is to use IE for grading and only one grader may be logged in at any time.

Really, fire is too good for this mess.

Curious, how would you do that? Would it be a long script or is there some sort of mini Library for this?

Browser extension is easiest, https://addons.mozilla.org/en-US/firefox/addon/greasemonkey/