So if you follow what's happening. A person *could* change the shipping method. If they do that, the form is refreshed, and the cart is displayed with that new ship method. No problem there. They could also leave the shipping method as it was, and add a comment and authorize the payment. No problem there either. BUT if a person leaves a comment, then decides to also change the shipment method, that comment then disappears and they are forced to enter it again.
I really don't want to split this into two pages, and it's absolutely necessary that these two options are given. This is actually a page from a PayPal Express payment. The customer accesses PayPal, PalPal sends them to this page after verification, then this page sends the data to PayPal to finalize it.
I hope I didn't make this more complicated than it is.
I don't understand what you're doing well enough to really make much of a suggestion, except use a bit of AJAX to update the cart rather than refreshing the page to change the selection value of the form... Otherwise I'll have to understand the system a bit better, because I'm sure there's a reason, but I can't see why you need to have the two forms, or at least the entry sections separated.
IMO You could easily use AJAX to update anything you are updating with a full page refresh (form submission), but I really don't understand what you are doing very well.