Big Box insulation foam is NOT a viable choice. Too soft, too porous. Even if you could manage to get a decent finish on it, you'll just be replacing it a lot. Plus all the insulation foam available at the Big Boxes in my area is prescored for breaking it apart.

Sign Foam or HDU is a decent choice, but you'll have to get it from a sign supply, and it isn't cheap. It does carve and finish well, but it is also susceptible to damage in high winds or hail.

Home Depots in my area sell 1/2" pvc sheets (like Sintra or Komatex) which would work. it's not as dense as what you can get from a sign supply, but it carves well and finishes well. There's a lot of info out there on the webs on how to finish it. I wouldn't ask for advice on how to finish it here since you mentioned the "d" or "v" word.