Being on the Xbox 360 you have 2 choices........
1/. You can start a new character & go for all the Masks & Keep them or
2/. You just deal with the fact & move on with your current character, because as MushroomGenius stated
.
I realise that for a lot of people, making a new character isn't the answer they were seeking & most wouldn't even consider doing that. But for some of us it's the only option. On my first 3 characters I only kept a couple of the masks & sold the rest.
On my 12th or 13th character I actually went for all of them, I haven't got them all yet ( I have 2 to go ) as I'm now playing on a new character on an Unpatched Skyrim to assess the differences in some of the Quest Problems that have arisen since the Patches were released.