So after I recommended leaving more space between the strings to avoid buying 24 brads, I tried it that way. And now I'm mad at myself for not doing that before!
Only doing 3 strips of ribbon each direction instead of 5 means you only need 5 brads instead of 13. A-Ha!
Here are the boards I whipped up tonight. I couldn't quite do 10 - I ran out of ribbon and my hand hurts from squeezing the staple gun, but I finished 7. The small ones are 11x14, and I made 2 16x20 toiles with leftovers from Bonnie's curtains: