Leaving currency at the exchange is akin to trusting bank/third party.
What are your thoughts. Is this problem solvable?
It is literally already solved.
EDIT:
Proposal:
buy 6 different 8gb flash drives for $40 or less, backup the encrypted wallet on each of them, with a printed piece of paper with the wallet. Buy a $50 fireproof lockbox and keep the key with your regular car/apt keys. Boom, redundancy. All for less than a hundred bucks.