How to add insulation to a hollow core exterior door?
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.