Not a developer, but I wrote Redemption Rift, so let's see what I can remember...
Note, IIRC, Rift pre-dates the Field Manual, and any TOE work I did for Rift would have been from extant Wizkids sources. Which were kind of a mess. And I was not involved in the Field Manual, so if it differs from Rift, that's just the progression of time, since I think Rift was set about 5 years earlier.
Hack Kincaid never commanded Gamma; if Rift says that, it's wrong. He was colonel in charge of all striker battalions.
I believe there was a Gamma Regiment, complete; an Alpha Regiment, which was primarily training and administrative, but which contained the Black Cats battalion (a Wizkids one-off mention, IIRC), which was not a striker battalion. I don't recall whether Beta existed then or not.
There were then, I think, three striker battalions at the end of Rift? The Spider's Web, the Tarantulas, the Wolfsbane. Separate units from the line regiment(s).
And yes, the strikers had odd TOEs because that was still in the days of Wizkids' conception of combat, when you had "armies" rather than formed lances and companies. So I leaned in and created an administrative "company" that would make a decent "army" on tabletop... I think.
I've slept since then.