My soil is a lot like yours from the rock aspect. I get every size rock from marbles to Volkswagens (and every size in between) when I dig here.
I built a 3 ft by 6 foot frame and nailed 1/2 inch mesh, welded wire onto it, with some trim to protect the edges and legs and braces to set a desired angle.
Any time I am going to get into any serious digging (especially when I'm building a new garden) I dig the entire area to a depth of
at least a foot, and pitch each shovelful through the screen. The rocks roll down to the base of the sifter (or into a wagon) where they are carted off to be used for potholes, paths or rock borders.
Add your compost to your mound of sifted soil, mix well, and redistribute the soil over the area. Voila!
I also use the sifter to take the course matter out of my compost. The wheelbarrow fits right under the screen, so your sifted compost will be loaded and ready to go....