It's 3mm flat reed. I love the narrow channels too. I did 3/8" channels at the center front and back next to the eyelets and cut a 1/2" half-oval or flat reed down to fit. It's the same stuff I used on my 1690's stays last year, and I was happy with it the one time I got to wear them.

They said they're planning another ball so I have that to look forward to, but it's a mystery when it will be or what period! They did a colonial ball in October and a Regency ball in April. As long as it's not Renaissance, I think I'll be able to find something in my wardrobe to wear if they go with such broad categories.