I would like to see backpack as a "powerup"(it can always be explained that player had found new backpack with lots of pockets especially for ammo). New special level is always interesting to clear, also special level prevents from taking backpack early in game(for example, on Nightmare!, you can raise your level to 10 easily on dlvl 2). IMHO this special level must be approximately at dlvl 9(not too early, and not too late). Also it looks like original DooM backpack then. Also new special level means more exp, which is good!
Why not trait? I have already many traits, that i want to take(and usually i don't have ability to take all i need), and i think that making backpack a trait will force you or to loose levels, that you can spent on more practical traits, or not to use it at all(if you cannot successfully use weapon, then for what you need more ammo for it?).