A couple of further comments here:

Hugo theorized that if the bridge chip believe that it was master, and that there was no slave, it might never release the bus. This seemed to be the case, since setting either the CS or Slave jumper allowed the ethernet to enumerate. Unfortunately, it also caused the SSD to enumerate as /dev/hdb, which would require some futzing to fix.

More interestingly, the $30 Aleratec PATA<>mSATA bridge with the nice Marvell chip displayed the bad behaviour, but the $7 bridge with the cheap JMicron bridge chip works great.

I stepped down to a 250GB SSD because it's large enough, and avoids the memory challenges that mlord mentioned around the 500GB. So far, so good. Time to load All The Music and see how it goes.