I don't know if anyone is following this thread anymore, but just in case someone else has similar problems:
For the sake of it, I reformatted partitions on the new DMS and loaded music using Media Manager 3.76, instead of Music Manager 2.30 that I've been using until now. I also let it save in the old database format on the DMS, as is recommended.
This solves the problem of it failing to start up at first after starting the car. It starts up and plays fine now. But it creates a whole new problem: Now the disk random function doesn't work. When I enable it, it spins through the playlists, then I get "eject" on the head unit once again. And nothing will make it work -- if I cycle through the sources on the head unit, all it will do is start the track that had been playing. As a further side effect, if disk random is enabled, I cannot fast forward or rewind within a track.
I use disk random almost exclusively, so I will probably have to go back to Music Manager (probably have to reformat too) and put up with the first problem.
I'm still thinking this is a Hitachi disk issue, but I'd sure welcome further suggestions.