Yes, you can't change the settings of your webinar program after you have added persons to the program. But you can do that, after you your program is devoid of members again. So here's what I would do:
Add your program members to a list. (You might have that list of registrants already, if you have an Add to List flow step in your Registration Tracking campaign).
Remove them from the program (Change Program Status --> New Status: Not in Program)
Change your webinar adapter settings
Re-add the list members to the program with the status of "Registered". That will trigger the API call to GTW where they will become registered.
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