20 tons isn't that much to do. Have the first dump at or near the top or house and the second about 1/2 way to the road. The box holds more than the bucket so you won't use the bucket much. If you can get at least a hydraulic top link things will be much easier. Otherwise set the box about 1/4"-1/2" from cutting while going forward. Back into pile, bury and fill box, then drag and spread as you go.
Once everything is prepped with an edge along your driveway and smooth, spreading this should be a nice little project that will take less than a day to spread.
Btw- I would rarely have the dump and spread routine done. Far to many variables and in my area the drivers were an unknown as well. I'm not saying it doesn't have a place. Just with a little drive like this it isn't saving much.
You will also want some size in the material delivered. Typically it's 5/8" or 3/4" minus. I'm not sure what your plant is calling crusher and I don't think all 1/4" minus is best for a road.