Ugh, this is a retrospective attempt to clean up all the dribble I wrote.  My IIe clearly has a power supply issue.  In the middle of this process (after I had reseated the Disk ][ controller but in fairness also after I had powered it on successfully), the red LED would flicker and it clicked.  This stopped when I reseated the Disk ][ cable on the card itself.  In case anyone has to investigate recapping the PSU I did find this when I figured I'd have to: http://obsolescenceguaranteed.blogspot.com/2014/03/bad-caps-or-recap-kids-apple-iie-power.html