Hi Nancy, honestly I don't have vast experience with design for screen readers. Your suggestion sounds like an interesting way of tackling the challenge.
What I would do to make sure it works is to user test the solution. Try testing with 6–7 users who are using screen readers. See if they have problems understanding the information and if any problem patterns emerge from the tests. Then it becomes easier to adjust the information architecture.
Thanks for taking the time to read the article!