I prototype almost everything that I do in foam first. You can get much smoother results than that right off the CNC. What bit did you use and what were your feeds and speeds? As an example, here is a pic of the results that you can easily attain.
This is with no sanding or post carve processing.
What bit did YOU use?
The carvings for the tombstones are
White Z = 0
Black Z = 1
Cut speed:
a RIDICULOUS 800 inches per minute
For this test, I bought round router bits and did an initial test by scaling the Z to 10%. It carved the face nice and smooth, but there was almost no definition. So JUST to see if this would work, I switched to a rotary RASP

and let it carve the full 1" depth in a single pass. Obviously it chewed up the foam but it cut much faster, and gave me these results.
The V shape of the rasp created more problems as the bit plunged to the correct depth, but also carved away at the sides of material that was NOT supposed to be removed.
I would love to find something like this, with a rasp cutting surface, a longer shank, and two full inches of cutting depth along the shank, and a round cutting bottom for plunges!
I am using my Samson 510 table and DesignEdge software. It is intended for single plane CNC plasma cutting, so I cannot set up the router to do deep cuts in several passes, and I cannot find a round tip two-flute bit that will cut 1" deep SIDEWAYS.
Someone needs to design and sell bits specifically made for FOAM, since a 1" plunge into the material and carving in a single pass will NOT overload the router with X and Y movements!
The round ball bits WILL cut that deep, but of course the material ABOVE the ball's cut path must be removed first for the deeper cuts.
So I may switch back to the round ball and then cut the face at 10%, and a second pass at 25% scaling of Z in the pattern, and then maybe 50%, and so forth, to see if I can eventually get down to the depth I seek.
Also, DesignEdge sets the depth of their "3D" cuts by gradients in the image, so as the colors of the tombstone get lighter and darker, the software reads this as +/- Z settings. So the MAIN PROBLEM with this is that I do not have a good cut file is based on actual contours rather than gradient values.
I will try again today, with a different bit and a different technique.
I have V-Carve PRO, but I am not familiar with
how to import a photo such as the one above and have the software SLICE that into passes, using a 1/4" two flute bit to hog out the meat, before coming back with a final pass with the correct bit and a much narrower step-over setting.
Joe