I believe that the answer to your question is that it is illegal to stash (cache) anything in the park. I'm too lazy to look it up, but I know I've seen it in the rules.

That said, I've found other people's caches. I've never known what the proper response should be. Usually, I leave it alone and report locations upon leaving the park.

The option of exiting to reload requires a new permit. The option of setting up a Rendezvous could be problematic if something unforeseen causes either party to miss the connection. Probably, the safest option is to carry it all or to preplan that 2nd permit.

See ya at Copia  ;)