Awesome! :D
Thomas, I like your ideas for different arenas, although a few of them are too similar for my taste (AK/Hardcore and Endurance/Death). :)
Maybe replace those two with "Deathmatch Arenas" that mimic real Doom multiplayer? That is, instead of fighting hordes of monsters, you're fighting against a handful of Doom marines just like you.
Everyone starts out the same, with a pistol and a green armor, and you run for weapons and ammo (that regenerate). Get the most number of frags in a given amount of time!
Another idea! Co-op is always super fun... now, it would really mess up the rhythm of the normal game, but could be perfect for Arena modes. I would call it "Two Versus Many" or something like that. Essentially it is you and one other Doom marine against the hordes. It'd be nice to finally have someone on your side for once!
The AI could check if you're low on health and drop a health pack for you, blast enemies that are threatening you, or otherwise just help you out. He could also ask YOU for help...
Former human sargeant shoots. Kornel is hit! Kornel says "Help, I need some cover fire over here!"
Another possibility is Team Deathmatch (2 v 2 or 4 v 4).
I don't know, this is probably going overboard. It would be fun, though. :)