Painting Reticulated Foam

[BorkWockaMeep]

Hello Everyone!
So, I have a project to make a monster burrito, and I don't want to cover him with fleece. Instead, I want to paint his details like Miss Piggy. But, I am not sure exactly how to go about that. With what I have seen, the seams which the foam is glued together looks like they won't be hidden very well :/ How do they do it so well??
Your help would be much appreciated!

~BoWoMe

 

[Muppetlab]

Maybe carve it so there are no seams?