I have solid clay under just a couple inches of sod. I've found that most trees and shrubs don't do well for me if planted after digging down and amending the soil.
So my strategy is to lift out the sod/turf, thoroughly fork and fracture the clay subsoil, add a layer of half finished, unscreened compost, including sticks and earthworms, return the sod chopped up into chunks grass-side down, sprinkle some pea gravel and a thin buffer layer of the mound soil mix on the sod-bottom-clay, put the rootball of the tree/shrub on top, making sure to loosen the roots (tucking longer roots in between the sod chunks), then mound a mix made of up no-frills clay-y topsoil (unamended but better than solid clay) from elsewhere in the garden, screened finished compost and some sand. In other words, I plant the trees on mounds.
Depending on water requirements of the tree and the lay of the land, I leave a shallow swale on the upslope side of the planting to sequester water for the drought we always have in the summer, and if necessary, raise a slight mound on the downslope side to hold water (broken or solid quarter circle~semi-circle). Otherwise, water can drain away right along the top of the clay subsoil and leave the mound dry.
As I finish the mound, I fork the area and lay wet cardboard in a circle surrounding the tree to sheet mulch, then mulch and stake the tree two-, three-, or four-way as necessary.
So far, this method has produced good results.