Hi @gdavies
Thanks for reaching out to us and welcome to our community!
It looks like you could benefit from the Server to Server OAuth app type:
Basically the only thing that changes between the JWT app and the Server to Server OAuth app is the token generation.
Here is a migration guide:
And also a post on how to user Server to Server Oauth app with Postman that could be a good starting point for you
Hope this helps!
Elisa