Healthy visions for a suffocating yard

Question: Hello! 
 
I am currently removing landscaping plastic from my backyard. It appears the previous owners thought white stretchy plastic would be a good idea (probably 15 years ago), which they covered with a (now super thin) layer of mulch which has accumulated a good 3-4 inches of clay over it, with a healthy smattering of 3/4 in river rocks mixed into it. A month ago, when I started, the rocks make it impossible to use anything other than a hand spade to get through!
 
To my delight, I’ve found that the dry weather has conveniently caused the clay to crack, so I’ve been able to pull plates of the stuff up to expose the mulch (and likely old topsoil) layer, which I’m able to gently remove with a hand spade to expose the plastic and peel back. I’ve made it down our 100 ft fence line over the last couple weekends, and am now doubling back perpendicularly, so that I can toss the soil where I’ve already been. 
 
So now I’ve got a healthy pile of clay ‘chunks’ that are starting to pile up, and the earth beneath the plastic is even more clay and rocks! I feel like I might be piling one problem onto another.
 
With that context, I’m wondering how to deal with (a) the pile of clay chunks (do I water them and then use a rototiller, or do I need to pull out my trusty pickaxe to break it down?) and (b) the soil underneath concerns me! I’m sure it will crack too now that it’s exposed to the elements. Do I leave it and add good stuff on top? If I go this route, how deep of the good stuff (and what) should I be so side ring (ie should I shave it down to account for 4 inches of compost) …
 
The plastic removal project is a big one, and will likely take me thru October at the rate I’m going (that’s okay, the excuse to be outside is a welcome one after our rainy winter and spring!). My goal however is by next spring I’d like to start landscaping the area. So another question (c) is: Over the winter, what can I do to prepare the space?
 
Do you have any other tips or rabbit holes I could dive into?
 
Many thanks!

responder: The Question Asker Replied May 29, 2023, 8:26 PM EDT
response: Typo! In question b! It says ‘… should I be so side ring,’ but it should say ‘should I be considering…’   Auto-correct failed me!

responder: Linda J. Brewer, Senior Faculty Research Assistant II  Replied May 30, 2023, 1:46 PM EDT
response: Dear Katy Ahlvin:  Thirty-five years ago, I was in exactly your position, and I have lived to tell the tale. Well, I only had a space that was 80' X 6', but still.   My biggest message to you is that we have clay soils in this part of the valley due to geologic actions taking place at the end of the last ice age - 10,000-18,000 years ago.  Like diamonds, clay soils are forever. I still live on that same Benton County property, and have just learned to live with clay soils. They are not bad, not heavy, just high clay content.   Why not read up on hugel beet culture or lasagna beds? This has been the key to my success. Please don't think about tilling anything into the soil. The best you can do is spread it on top and let the tincture of time change the conditions below. MOST OF ALL don't let anybody talk you into adding sand to the soil.  With those clay chunks you have choices. You could just stack them up and make them a part of your raised planting beds. And you could include some brought in soil as part of your beds. I realize that's not in your original plan, but just putting 4 inches of soil on top of the clay will give you a 4 inch planting depth. Alternatively, they could just go into the yard debris cart.   Above all, look around the neighborhood to identify plants that are doing well. There are lots of plants that I would like to put in my landscape, but it would just be a waste of money. If they require rapid drainage, they're not going to survive over time.