Oh cool, are they going to do 12 pcs, all different materials and cuts? That's how just about every crossfit gym has worked out around here for us.
You might be able to print that in 4 colors plus a single white. You're going to lose some of the colors, but i don't think it will be that noticeable.
Have you thought about transfers for the center icon? Print the white, then line up the transfers to make them work. We did this on a job with a 4 color nape of neck logo. It worked out better to print the back, print a smaller outline of the logo for placement and heat press the logo in place.