The solution: I've been chipping away at it, day by day, as a nice afternoon break from office work. It's remarkable how wonderful it is to take a pitchfork and drive it into that stuff; there's something about good physical labor that really helps clear one's mind at the end of a long day.
One wheelbarow load at a time, I've been taking it from the barn to my vineyard that's fairly close by. I'm averaging about 2-3 wheelbarow loads per day. I think that's the key lesson I've learned from trying combine a small farm with a small consulting practice: stop waiting for a big chunk of time before you tackle a project, and don't be afraid to do a little at a time. Bit by bit, that horrible old bedding is disappearing --- and, one row at a time, the vineyard is getting mulched. Here is Double Play, hanging out on what's left of the old bedding. Note how deep it is, and how much is still left to do.
The stuff at the bottom of the bedding is basically composted, it's so far deteriorated. Closer to the top, it's still basically rotting hay and straw. While not perfect organic compost that could be used in the garden, it makes a nice mulch for the vineyard. The composted portion provides nutrients for the soil, while the intact portion blocks weeds and absorbs rainwater. And over time, the rainwater will slowly leach additional nutrients out of the mulch and into the vineyard soil.