IMIM2 said:
Now I'm interested.
There are two things here:
1. You said you successfully transfer an image on the smooth side. Mind sharing that?
2. To make pattern, the fabricator use hot mold and press against the foam. Heat will close the pores, therefore ink/dye will not stick to it.
What I have in mind (still in theory):
a. Sanding it lightly (but it has the risk of ruining the pattern)
b. cover it with paper/paper mache (I don't know how conformable paper to the pattern)
c. do fabric printing, and glue it to the patterned foam, and use pressure so the fabric is conformed with the pattern.
d. try to ruin the foam surface chemically (acetone/porcelain cleaner/acid?) lightly and wash it quickly.