Amazon has finally gotten back to me, and seems to acknowledge that their current inventory is defective. They advise waiting a few days before re-ordering. Although it's hard to believe it of this great company, their plan seems to be to sell the defective units to other people, so I should wait a few days until they've done that. The syntax is a bit ESL, so perhaps I'm misunderstanding. It's posted below; you be the judge. In any case, I would suggest that anyone contemplating a purchase of an 880 from them heed their advice.

From Amazon:

My previous associate has contacted the fullfillment center to know
about the inventory of the item "Logitech Harmony 880 Remote
Control" and we learn that currently we have few set of this items
as "defective".

So, we are afraid to send another replacement assuming that it will
arrive defective again. I would request you to please wait for 2-3
days till we get the new inventory and you can place the new order
for this item.

As you know that the original package is returning to us and upon
receipt we will issue a full refund for the order including shipping
cost.

I understand that your are very upset, but believe me this is not
our normal practice. We always strive to give our customer the best
customer service. In this case we have not meet your expectations.

I would request you to please reorder the item again after 3 days
and I confirm that you will not receive the defective item again.