You have a good provenance for this coin. Mark Bir had a stock of ancients of very good quality, before his untimely death.
That's a really nice new style tetradrachm. The centering of the reverse is definitely above average, and the metal quality is very good. In comparison, here is my Antiochus coin from the same period. 16.8 grams: Thompson dates the elephant reverse type to 168/2 BC. This coin has ABPΩN and a gamma ( Γ), the third month, Boidromion, on the amphora, which makes it a Thompson 397e, but with control mark ME below the amphora instead of ΣΦ, as listed in the catalog. Your coin has ΣKYMNOΣ and a epsilon (E), the fifth month, Maimakterion, on the amphora, which makes it a Thompson 397h, as you noted, but with control mark ME below the amphora instead of ΣΦ, as listed in the catalog. The months that I use here are based on the Athenian Civil Calendar. For information, here's a link: https://www.ancient.eu/article/833/the-athenian-calendar/ Given the extensive number of varieties for this type, I am not surprised about the difference in control marks. Here's a link to the Thompson catalog, courtesy of the Digital Library: http://numismatics.org/digitallibrary/ark:/53695/nnan131509