Ah. Just what I feared. I have an area like that that I HAVE converted into a rice paddy. It holds water for about 3 days without topping up under normally weather conditions. (Goes down a little faster in drought) Another area that I had hoped to turn into earth/clay-bottomed pond turned out to have just enough organic matter in the soil to be inefficient for holding water.
So, I see and remember now that you said you have lots of rocks. I was going to say I use the sod as a kind of berm and build up a mound on TOP of the ground to plant the tree in. I get mixed clay soil from elsewhere in the garden (like that pond I was digging).
I actually don't have too much time right now either, but the way I do this, briefly, is to fork the ground, like I said -- just fractures or holes, layer leaves and about 1" of HALF FINISHED compost, usually teaming with earthworms. I lay the turned over sod from the center circle cut up in a few pieces as a buffer to put the tree on (the roots go on the clay soil side), and the sod from the rest of the circle to build a berm (you could use your rocks) Then use unamended clay/loam soil (I don't want to give the tree too rich a soil or it'll get "spoiled" and won't learn to live in the clay, but I've also inoculated the ground under it with the compost microbes and earthworms to hopefully start the conversion process) to fill around and up to the tree's soil line. I use the turned over sod on top of the roots (if bareroot trees) to hold them in place.
I dig a swale (crescent shaped moat) upslope or downslope of the mound depending on water needs of the tree (downslope if well drained soil is needed, upslope if sensitive to being dried out). Then mulch the surrounding area with cardboard or layers of paper topped with leaves, straw, and/or hardwood mulch.
Because the entire root ball and tree are sitting on top of the clay with just a mound of clay soil around it the tree WILL need at least 2, possibly 3 stakes around it with guy lines (is that the right term? I use rope threaded through pieces of old garden hose to prevent damaging the tree).
For trees that REALLY need good drainage, I add pea gravel or -- ummm can't remember the name of it but it's the coarse sand used for patio projects -- some with the compost and some on top of the turned over sod.
Oh! and VERY IMPORTANT, I fork/fracture all around the edge of the hole and also all the ground around the hole before mulching.