Routing and Painting Sign Foam

We have been fairly successful in selling routed SignFoam signs. However, our method of painting seems very time consuming and labor intensive. We first rout the raw foam then seal and paint the entire piece the background color. We then apply the border and raised copy color by hand using a foam brush. This takes a lot of time and invariably leads to drips and runs that have to be touched up etc.

Has anyone had success painting the sign blank the raised copy and border color, covering the blank with a mask material, routing through the mask and, painting the background with the mask still in place. We don't do sandblasting in my shop but, I think this is the way sanblasters do their signs.

I would appreciate any tips to include type (brand name) of mask used, how to avoid the router bit clogging up with adhesive and mask material (maybe type and brand of router bit used) and any other information that could be helpful.