بَعْلَبَكّ is a single compound proper name made from «بَعْلَ» and «بَكّ».
بَعْلَ: first component, built on fatḥ in the book’s preferred analysis.
بَكّ: second component, declined like a diptote.
This is the proper name of a city, not an ordinary “first term + genitive term” construction. You need two different grammatical analyses within the one compound.