My first thought when reading the post was:
I had to re-read the post, to try and find out what the problem was....Either the OP forgot to list the issue, or I am not reading it.
The Rim joists serve as headers over that span. They are working. Why would you want to consider doing such major work on your home, when it is not needed? When there doesn't appear to be any problems?
No, it is not built by modern framing standards, but so are alot of other older homes that are still standing, and have not shown any signs of structural shifting.
Are you bored?