OK, I'm thinking there may be a way to get the judge to order the storage unit's facility to put another lock on the unit and maintain it in limbo till you get a court order to cut off his lock and find the stuff. You mgith want to get an emergency hearing on that since he's disappeared.
Some kind of injunction... a temporary injunction prohibiting access ... or heck, maybe there's a process for this.
I know if a storage unit owner dies, every state has a procedure for handling it... same as if it were a safe deposit box... like it gets totally locked so NO ONE can enter till a judge orders it.
There's got to be a way for you to get this to happen. Ask your lawyer. I'm surprised your lawyer didn't suggest this, to tell the truth. Maybe you didn't explain how worried you are about this? Or maybe they've never done it before... it's not something I'd think was very common!