A couple of thoughts. first, is the speaker plugged into the amp or hard-wired? You should be able to get a cable from BEST BUY or RADIO SHACK with the proper plug on one end to go into the amp and the other into the audio input of a VHS or DVD recorder. If you have a LINE OUT or similar type connection at the amp this will be a breeze. Otherwise the amp volume will have to be next to nothing (start with no volume and come up slowly, listening to the TV sound for best quality-you may have some krackle and distortion).
As for TV, a video camera on a tripod can work. You are not lip-syncronizing so the sound/picture match should not be a problem. Position the camera so all but the edges of the projector's frame appear on the TV screen when you get it, lock it down.
If you can get it on a VHS tape, I can copy the tape onto a DVD. Quality should be same as what is on the tape.
When you are all set, try a strip, play the recording back and see if you are happy with the quality.
DO NOT USE MICROPHONE TO SPEAKER IF YOU CAN AT ALL AVOID IT FOR CAPTURING SOUND!.
