PROBLEM AVERTED, according to an e-mail I just got:
After an overwhelming number of responses, it has been made clear to the FilePlanet team the value of these files, and so it has been decided that the file hosting services will NOT be retired as we had previously advised. To clarify, anything you have uploaded to FilePlanet as a hosted site owner *will remain on their servers indefinitely*, and your file URLs will once again be valid despite any error messages that may have been appearing over the last few days.
May we stress that the new plan is to retain hosted site file uploads indefinitely; should there ever be a need in the future to reconsider this, we will endeavour to provide adequate notice.
Time to do some testing, but that certainly saves me a headache for now. Thanks for the suggestions, all!