You do have to be a resident of the state where you are buying the gun, but I also do not have to have a DMV issued ID unless I want to operate a motor vehicle on public roads. The best way to prove residency is to show the inquirer your home

How does the formal libertarian feel about identification and having to carry your "papers"?
I would argue my way out of having proof of recidency by having to show a lease. You could easily be staying at an extended stay hotel in which there are no lease agreements. Also if you share a room with a spouse who paid and only has a receipt in their name, you have no written proof of you even being there. Plus, you can't put a hotel as your address.
There's so many holes in the residency requirements, and you can always do like me, and argue with people until they take what form of I.D. you are offering.
To get a storage unit, the most you'll need is an I.D. of any sort, if even that.
BTW, this might not be the law, but it works for me!