What is Zion?
Can you please define the word "is"?
Your mum's arse ranger outpost Your mum's arse
there really is no good place in Zion to store stuff or for player housing at that. You just gotta suck it up and take what you want most with your current weight limit. You can go back to Zion anyway later and get more stuff.
I would say drop it all in Lucky 38 or Motel room, then load your .357 Mag with 6 rounds and hope for the best.
I usually just used one of the boxes, or lockers in Stone Bones Cave...