First the earwigs came. Then the worms crawled in, the worms crawled out. The eyes bulged from their sockets. There was even some fuzzy mold after that. There might have been a slight odor of decomposition, but let's not dwell on that unpleasantness. I sprayed the skull a little with the "Jet" setting on the hose and unexpectedly excised the lens of the eye. At least, I think that's what it was. But the hose is not a precision instrument and bird skulls are pretty delicate, so I gave up the hose surgery endeavor. Still, much of the skull was covered with bits of dried skin and tiny feathers as well as the cartilaginous bits that had supported the eye (on the side I hadn't blasted with the hose).
I decided to boil it. When you boil a chicken carcass it eventually comes pretty clean, right? And also - true story - when I told my neighbor about my cardinal head treasure, she told me about how she boiled a penguin head (super envious) she'd found on a beach years ago; that's how she got it clean. (You see why I like living in Vermont?)
So I took my camping stove and an old camping pot that's too small to be useful and I made rotten cardinal-head soup. Unfortunately I accidentally deleted the two pictures I took of that. I did it outside so that any smells would dissipate on the wind. I boiled the skull for about an hour, maybe occasionally picking bits of skin and feathers off as I could (I wore gloves, but again, let's not discuss such unpleasantness) and then just left it in the garage for another week while I was away visiting my family near Buffalo.
This is what it looks like now. Skulls are so cool.