Before I contact White Oak, does anyone know what the difference is between WOA's "varmint chamber" and a Wylde chamber?

Directly from WOA...."Our varmint chamber is simply a modified Wylde chamber, we shorten the throat of the Wylde slightly.  You can treat it like Wydle, it shoots both .223 and 5.56."

I don't have specific experience with that as I only have one of their Wylde chambers, but the comment in your second post sounds accurate enough.

The Wylde chamber is liked by precision shooters because of the longer throat which allows for longer bullets to be seated (likely to be loaded one at a time and not through a mag). If they shorten it, it means being able to get closer to the lands while staying within magazine lengths.

My Wylde chamber using 77gr SMKs measured out to around 2.000" base to ogive while magazine length on the same rounds measured to around 1.880" (SMKs have inconsistent tips). I'm being forced to jump by a whopping 120 thousandths!

If their varmint chamber is closer to that 1.880", it might improve accuracy potential.

I will say though, the Wylde chamber is working very well for me but is pickier about loads than something like my 223 bolt gun.