Think I found the patch we've been digging for. The Air Force also wears the Army's "multicam" uniform as of Oct 1st

https://www.military.com/daily-news/2018/05/14/its-official-air-force-switching-armys-ocp-uniform.html

Unit patches don't often change over time, but the 436 Tactical Fighter Training Squadron has all the elements in the pic (PB); Downward sword, wings and a spade.