I purchased a new 3930CI, and will install by tomorrow.  Eagerly looking forward to testing, and see if the problems described above are gone (I hope, I hope, I hope!!!).  
 
 
ButterflyPhoto.com won't give me a refund, only replace my misbehaving unit.  As soon as I install my new player, I'll return the bad unit to ButterflyPhoto, receive a new replacement unit, and then sell it on eBay.
I did confirm the unexpected behavior is not caused by the source (DVD), or the HDMI cable.  Only things remaining are the player or HDMI board I installed.  After speaking w/ Panasonic tech support, I don't believe the HDMI board is the cause - probably the player.