Jeffro, your case is well-presented but the destruction of Beth-Shean is not related to the destruction of Gath in 830.
Archaeomagnetic results indicate that Beth-Shean was probably destroyed at the same time as Tevet VII and Rehov V, not Gath. The fact that Shoshenq depicted Rehov and Beth-Shean side by side as prisoners of war in his Triumphal Relief at Karnak (Egypt), shows they were both destroyed in his campaigns.
When was that? None of those are historically dated chronological anchors in the study, but radiocarbon dating indicates Rehov V was destroyed by fire in the late tenth to early ninth century, possibly ca.900 BCE. Based on this dating, the study concludes:
Archaeomagnetic dating of Beth-Shean shows that at a 95% confidence level the destruction occurred before ca. 880 BCE and at a 68% confidence level it occurred before ca. 900 BCE.