Doors – Noise reduction of a hollow core door versus a french (glass panes) door

Polyurethane Foam. The type that is used for insulation.

1. Remove the door, remove knob and screw
2. Tape rear hole to contain foam.
3. Lay door flat
4. Enlarge knob hole to allow dispensing wand to fit. (If this enlargment is too close to the knob base size, this method won't work)
5. Dispense foam into hole. Probably a 3-4 second burst will be enough
6. After curing overnight, redrill the hole to allow screw to pass.

This works because the foam will keep the hollow walls from collapsing

I think you've hit on the easiest solution. Putting in a layer of insulation board and then boarding over the top of that is the approach I'd take.

If you don't want to use the door then you can just put insulation right to the frame and board over that to hide the door completely. However, if you want to be able to use the door then you'd have to leave enough space at the edges so that the door could open without catching on the frame.

Insulation board is quite light so you'll probably be able to glue a frame to the door an inch or so in from the sides and then put the insulation in that. A piece of hardboard glued or tacked over the top will keep the board in place. This will mean that there is still some heat leakage around the sides but nowhere near as much as through the entire door.