Diesel fuel makes a dandy crud cutter.
Go buy a large rubbermaid tub of adequate size to hold the head, and a gas can.
You 3/4 fill the gas can with diesel. Take it home and slosh some in the rubber maid tub. Clean to your hearts content. Let it sit for a little bit, and return the diesel fuel to the gas can for future reuse.
Lacquer thinner makes an even better cleaner, but it's more expensive and evaporates a whole lot quicker. It also eats some plastics, making a remarkable mess.