Well it's a 120GB HDD and i've got the luck that i've got 2 xbox's (roommate has another 1) and tried it on both of them using the same HDD because the other one is only a 20GB HDD. With all DLC and patches on it the loading times on both xbox's takes aprox 5 min (also loading Singleplayer games =S )
So i tried removing all DLC and patches, deleted the Cache again and started the game up. Than you're required to patch the game in order to play MP.
After the patching I started up a game of Rush in Metro MP and it worked instantly, short loading (like 30 sec or less).
FYI, 1 xbox is using wireless the other one is connected to the router via cable (this didn't effect the loading while I was trying to load the game of rush in MP)
The game doesn't freeze during gameplay or loading (the dot on the lower righthand corner keeps blinking)
The free space i've got left on the 120 GB HDD is around: 81,11 GB
You are doing everything correly for troubleshooting the console; I can't think of any reason why your 360 would behave this way only with the DLC present. Skyrim was the only game that even came close to what you were describing, but that was only after several hours of play where the console would heat up. I put my 360S on a laptop cooler while playing Skryim and that solved the problem on that game for me.
My only recommendation at this point would be to make sure your console is in a well ventilated area, clean and free of dust and to call customer support since a Game Advisor might have seen this problem before. You can contact a GA here: EA Customer support: https://help.ea.com/contact-us
When you call make sure that you choose the "call me" option on the right so the GA wil call you when your place in the queue is up and you won't have to wait on the phone for an hour.
