Graev: I break out but it's impossible to dodge to the right to get my weapons. I keep getting smacked down no matter what. Anybody experience this?
Yes, the problem is that your dodge skill is too low.
Due to how incredibly easy combat is in the QFG series, most people just end up spamming attacks without ever defending to win battles, and due to the way stats gains work in this game any stat you aren't using doesn't rise at all. This all means that the
one time in the entire game where the stat is actually relevant it's way too low and it's too late to go back and grind it up!
Reload a save and do some practice rounds with Uhura without attacking. Just keep sidestepping until you're out of stamina. This will get your dodge skill high enough that you should succeed in the EOF challenge on the first try.