I think...

...that we have baby woodpeckers because I spent several hours outside
today (pics in a bit) and Lord and Lady Downey kept trading off shifts. One
would fly off for a while, then come back and call, at which time the other
one would emerge from the hole and fly off. The first one would then go
down in the hole. I couldn't quite tell if the arriving one was carrying an
insect or not.

The internet tells me fledglings leave the nest in about a month, so we're
planning on taking off some of the dead limbs that look like they might
fall in the future at that time. Leaving the one with the nest hole, of
course.