I have put some thought into this as my brother-in-law, who is a paramedic, said he'd love to see someone create this type of business so people's stories and wisdom doesn't die with them.

From your question, you stress that the main focus should be for the interviewee to feel listened to, socially connected and feel validated. This is an excellent central vision to ensure that making money from the venture isn't the main purpose that comes across.

Apart from the interviewee, I would see the customers as their family, historians, their friends/community groups and some themed groups.

When thinking of themed groups, I thought that a pre-interview (similar to what Andrew Warner does with Mixergy interviews) would help identify opportunities in this area. You will find that most person have skills, stories and ideas in areas such as art, cars, craft, life success (in money, health and wisdom) etc and this could be of interest to groups if compiled together. An example may be 20 people's stories on how they approach quilting or another group's stories on how they restored hot rods. To categorize these parts of the interview could show a powerful snapshot of that particular topic.

I hope this gives you a few ideas on how to potentially use (with permission) your collected content to add value to other's lives.