We need some out of the box ideas for revenue streams - a way to fund a service for the elderly that people are unlikely to pay for upfront.

Have you watched Jonathan Fields' Good Life Project http://www.goodlifeproject.com/

Maybe that'll get you some ideas and inspiration.
I know Jonathan and could connect you. I may have some other ideas but would need more information to know if they'd be worth trying.
Let's connect

This seems like a service that some families would pay for. I wish I could have had the story of my grandparents memorialized like this so that their stories didn't have to die with them. Why not do these video interviews as paid interviews...and create pricing so that for every one that you do, you also offer a free one to someone who can't afford it? It's kind of like Tom's Shoes, for every pair purchased, another pair is sent to a third world country. The free versions are the ones where you could furrow out the people you want to feature in your book....as well, you may also find interesting stories from the paid versions...in which case you could ask if the stories may be featured in the book. It seems like this could end up being a win-win business.

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.