Conceptually the GET should take those parameters, and it should respond with the page you want. That page only remembers those parameters if you tell it to (storing in a custom field is a good way for it to remember). The post isn't really related to the GET at all, so putting them in a field on the page seems a good way to remember them.
Assuming these parameters are in the URL, you could try reading from them in some client script on save, but that really isn't any better than just remembering/storing them on the page in the first place