"I think it is important to note that these were not public performances."

Not really any difference. You are recording an individual whether it is at the kitchen table or Carnegie Hall. Granted there are probabably fewer union regs to deal with in the kitchen.

"The recordings, and the rights to the recordings, belong to the person who made the recordings"

Not exactly. The person who made the recording only owns the physical tape and not the content. The voice that is recorded on it has rights, just as the composer and any musician on the recording. Unless you have a signed release, you cannot do with it as you see fit.

The "ethical" and "legal" way around this is to ATTEMPT to get permission from those who are on the recording, or their families. IF you do not have contact and cannot find them on the internet, you take your chance. In all probability there will be no issues, and the worst would be a request to remove the recording.   There is no cost involved, no money is exchanging hands, and no one needs to be "paid" for their release.