Just buy a preowned hard drive, the really cheap now. I dont have enough space for GTA and BF4 (going by the size of BF3 with DLC). So its what I plan on doing Put your profile data on a memory unit to stop the faff of switching it around every time.
I'm using the Xbox elite so my hard driver are the older version. If the newer xbox's use that part of hard drive then you've got the right idea. But Im not giving the advice to go buy the hard drive, not until someone with the same Xbox as you give the same advice.
You just may have to download your profile data on to the hard drive, or put all your files on to it.