Here's the scoop on MDs and ATRAC.
You CAN record something on a brand new ATRAC3 recorder and transfer it on older ATRAC firmwares ONLY if the recording is made in the STEREO setting. As mentioned, LP modes will not work, but you should not be using those for live taping anyway, non issue here.
The problem is that ATRAC has come a long way since 1995 (or whenever). If you take a tape made on an old school recorder and play it back on a new player, the sound will be limited by the ATRAC version it was originally recorded on. Also, a stereo tape made on a new ATRAC3 recorder and played back on an old version of ATRAC will be limited by the version of ATRAC that it is played back through.
It's a hard concept to understand, in the end, the better the gear on both ends of the tape, the better the overall sound. I think you're better off getting a higher end MD deck for playback/conversion. The MZ1 deck is a nice piece of nostalgia, but it's awful for our taping purposes.
Hope that makes sense.