I have had some luck with volunteers who can handle this sort of thing. In my case, there have been both those who have done the work in house and others who have taken the items home to work on at their leisure. I wouldn't recommend that tapes be entrusted to just anyone, but I have been fortunate to have volunteers whom I can trust. If these folks have some tie to the library -- as members of the Friends group or board, as longstanding volunteers in some other capacity or as simply regular patrons whom you've gotten to know well over the years. In our case, I was fortunate to have a close relative of a staffer (the son-in-law of my assistant, who certainly would have clobbered him if he was remiss in his repair "duties"). He has since moved away and been replaced in that capacity by my Friends Group president (whom I also feel I can trust).
If these volunteer options were to dry up, a similar service is provided at low cost by the regional library system office (Mid-Hudson Library System). I know that not every state has such organizations, but for any library served by such a consortium, it might be a good idea to see if such a service is offered by the central office--or if it could be.
Hyde Park Free Library
PS-- An unrelated question. Why is it that so many postings on this listserv appear in a format that actually posts them twice in effect (in different fonts and with a lot of gibberish in between). I find it a little distracting. Forgive my ignorance, but it seems to have something to do with something called a MIME format. Maybe it's a "mime" because it imitates itself....?