You’re welcome!
Wikipedia has an article about the US Army Institute of Heraldry. It was formed in 1960 as the successor to a group that operated from 1918-60. The article describes their function and lists a website that will likely have have contact information. Maybe you can reach someone to address your case.
My other three guesses are pretty wild. But I (and others, I’ll bet,) are very interested in finding out the solution to your mystery.
A militaria collector that specializes in headgear from the early-to-mid-20th century may also be able to offer some insight. Especially if they are familiar with your beret’s manufacturer.