Exterior door is probably cheaper, or you can beef up and interior door with GG+MDF layer.
I was considering making one, with the raised panel cabinet door look. I just bought the router set of bits to do it. Figured I could layer MDF with GG in the center and then the skinnier door panels on top. Three layers with two layers of GG, MDF mass in the center, it should work well for sound. Pain the ass to build I am sure- But probably cost me a few hundred bucks versus $2300 I don't have
"Too much is almost enough. Anything in life worth doing is worth overdoing. Moderation is for cowards."