If you don't want to go full custom, you could start with a solid core door and give it a facelift. Really depends whether you need the non-theater side to match other doors.
The other option I considered but rejected was using a two panel MDF door that matches the others in our home. I was going to fill the theater side with bondo then add GG and MDF. But it didn't have the mass of the solid core or the 4 heavy duty hinges.
I started with this:
And ended up with this on the rec room side:
And this on the theater side:
I have not measured STC, but very little is audible outside the theater. Inside is deafeningly quiet. To be critical, I believe the weak points are the zero seals because there is no sound going through the 1 3/4" solid core with green glue and 3/4" MDF on the theater side.
Let us know what you decide