If you cannot find anyone to take the physical documents, I hope that you will be able to find a volunteer to scan each document, to save on a USB drive, and to post online if the documents do not refer to living people. It would be a shame for that much research to go to waste. And, he might have information in those four bins that can no longer be found anywhere else.
By converting them to electronic copies, they will no longer take up space. If many refer to the area covered by your family history center, then you might even consider offering access to the older documents online.
Many teenagers at high schools are required to volunteer in their community for credit with clubs and organizations. Maybe the local high school can help find a volunteer.
Another thought is the local Family History Center of the Latter Day Saints. Mormans might be willing to do the work.