Convert interior door to wall - or similar - to make separate unit

[J. Martin]

I have an interior doorway/door that I would like to seal off to make the room on the other side more private. I'm thinking at least for the next 6 months to year, but maybe longer. I would like to leave the existing doorway and framing in tact.

The main objective is to reduce the noise between the two rooms. The doorway frame has about 4 inches of depth to fill with insulation or something else to dampen the noise, or about 6 inches of depth if I remove the door (OK too.)

Objectives:

1) Reduce noise between two rooms. Sealing this doorway is OK and expected. Not needed as entrance/exit
2) Not remove or ruin existing doorway. Repainting and light repairs to replace are OK. Door can be removed
3) Cost under $200 ideally, including $25/hr labor. But flexible on price depending on solution
4) Look good. The rest of the apartment is remodeled, and the finish needs to look good. Not patchwork. No exposed tape. Nice!

What are your ideas?

Preliminarily, I was thinking:

1) Leave the doors, add a bunch of insulation, then add drywall or something similar over the outside, flush with the doorway.
2) Replace with some super low-noise door with weather and sound stripping around edge of door. Right now, there is about a half-inch gap on the bottom, due to settling of the building..

IDEAS form you handy folks out there?

@Daniel S. 

, have a suggestion?