A slightly different suggestion: SFO-JFK-HEL-CPH (AY) and get the train (from the airport to Gothenberg). You'd arrive CPH at 10:35am. If you could get the 11:06 train (should be OK if no checked bags - no immigration etc on HEL-CPH) then you'd arrive Göteborg Central at 15:15. If you drive I guess you might be able to do it slightly quicker.

(Danish train info here: http://www.rejseplanen.dk/bin/query.exe/en? )