Go to the storage unit and show them you have a job and can get it resolved. They likely will pull it off the auction block and re-schedule it for the next one. Even more convincing is if you can bring them a job offer letter. If nothing else, it will buy you another month to come up with the money.

Honestly $300 is not a huge amount in the grand scheme of things--maybe do a GoFund me? I'd be in for a few bucks.