The first kind of self-storage which already exists would need no FFL. Nevada already does this for Californians at several of the larger gun shops in Las Vegas. They keep and maintain the firearms for Californians. It's not 'self-storage'.
The second case was looked at by ATF some time ago for customers who owned "Title II" (NFA) firearms to store at an out of state location and they did issue an opinion that for Title II and unrestricted firearms, an FFL was needed.
Of course, the ATF now requires that even guys that refinish/bed wood stocks for firearms or jeweler/engravers need to have an FFL.
My idea would be like a bank vault full of safety deposit type boxes where the renter would have a key....................