The following sounds like you cannot use a single GPU to upgrade a deep discount (STLKG) fare to PE on the overwater segment and also to F on the domestic sector. This would require two instruments:
Members requesting to move to a United® Premium Plus seat only and who have domestic portions of their itinerary will not be automatically waitlisted for United First. To be waitlisted for United First on domestic portions of an international itinerary, use your Global Premier Upgrade to request an upgrade to the United Polaris business class cabin.