It's unsurprising that 25 year old hard drives are failing. It's surprising, though, that no one's done anything about it before now. Audio files are not large. Hard drives in 1999 were, what, 30-40GB at most?
Current state of the art for backup is LTO-9 tape, which is 18TB to a tape, and the tape costs around a hundred bucks (less in bulk). That means 600 90's hard drives could be backed up to a single LTO-9 tape. The most expensive part of the process would probably be connecting the hard drives and copying data off of them, but once you've done that, it's easy to make multiple LTO copies for essentially no cost, which lets you store them in different locations, etc., and the fact that they'll take up maybe one thousandth of the physical space/weight has to lead to pretty good savings over time.
LTO tapes have at least a 30 year lifespan, and they don't fail all at once like disk drives do, so just plan to copy the data onto new (larger capacity) LTO tapes in 15-20 years, and you're golden. That no one has thought of this for 25 years, and just allowed these hard drives to sit around and rot, is pure negligence.