What you describe is the way redirection is supposed to work. The server tells the client, “don’t go here, go over there”. It only sends the client to a new URL, it doesn’t resend the POST data.
Reverse proxies work by opening up a new connection to the IS and forwarding the data inside, possibly modifying it as it goes.
It seems like you need some sort of reverse proxy (IS in reverse invoke mode) or the ability to directly to the Integration Server.