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Appian loads the default values for a form every time it's reloaded, other than what you pass in as rule inputs. For this use case it's pretty easy to have your submit button pass a value out (via a new Rule Input) that you then save into your process instance, and pass back into the form (via the same rule input usually) when it's reloaded, and your logic on the form would simply need to reflect that it needs to default to a value that was passed-in from the process (if there was one), otherwise the normal default.
Thanks