Opportunity is missed by most people because it is dressed in overalls and looks like work. - Thomas Edison
We are moving more and more to having custom plastisol transfers made for us when it comes to tough materials like that. We have been burned so many times trying to get decent prints on rough material. A transfer comes out crisp and bright every single time.
Is that what you'd do?(I suck at multicolor transfers done in house, and they go out the door Friday)
if it's small quantities, you could always go sublimation.