I agree with Seedcorn. The first thing I'd do is get a soils analysis so you can see what you are working with. I'd call your county extension office to ask about getting an analysis. Each state is different but usually the most cost effective way to get a good report is through them and they can help you interpret it. Since it is at least partly clay you probably have most of the nutrients you need except maybe nitrogen and maybe one or two more. Nitrogen leaches out with water so it can be low. My main concern with a soils analysis would be the pH of the soil and just to see if there are any surprises. Sometimes pH can take a little while to adjust.
You probably know this already, when you work a wet clay it can set up as hard as a brick when it dries. If it gets wet it can be a sticky mess. As far as tilth (workability) clay is not great. One way to greatly improve the tilth of a clay soil is to add a lot of organic material. You don't add it just on top, it needs to be worked into the soil. I can't tell for sure but that may have a compacted crust which would need to be broken up. That's one advantage to some of those green manure crops they are talking about. If you can get them to grow on it the roots can break it up but that may take a little time. If you can turn them under, especially before they go to seed, you can help yourself.
A lot of us have greatly improved the quality of our soil by adding organic matter, whether clay soil or sandy soil. That organic matter could be from green manure but you are somewhat limited in volume from how much you can grow on the spot. Some other stuff you can use is animal manure, grass cuttings, dead leaves, hay, straw, really about anything organic. Those wood chips will work too but some wood decomposes faster than others. If that arborist was chipping oak those might last a lot longer than if he were chipping a sycamore. But since you got them last fall they have probably started breaking down. They probably would be a good choice, especially of you can work them into the ground. Some wood chips I get from utilities trimming trees break down in a season, some last two seasons.
To break down into compost the organisms that do the actual breaking down need some moisture. In climates drier than yours some people like @digits just about have to bury their stuff to get it to break down. In Pennsylvania you should be wet enough that it will break down on top of the soil but watering it in dry weather can speed up the process. Or burying it to start with.
You are trying to change the character of the soil there. You are not going to do that with tiny amounts of organic matter. Don't be afraid to think big and pile it on really thick. Once you transform it you can cut back to a maintenance level.
I'd avoid putting organic matter on there that is diseased or a noxious weed that could make seeds or come back from roots. This one's more tricky because you need to know your bugs and their lifestyle, but if the crop is infected with a bug that overwinters in the soil you probably don't want to use that. I mentioned hay above, that can put a lot of seeds in the soil but some hay varieties might be more of a problem than others because od the types of seed.
People mentioned Red Clover and Crimson Clover. I think I remember correctly, I'd have to look it up to confirm, but one will come back from the roots in your climate, the other probably won't. I think Crimson is the one that will probably die out so it might be the better choice if you go with a clover.
I mostly remember
@baymule working on her sugar sand with organic matter. I think it took her three years before she got it to where she was fairly happy and trust me, Bay can lay it on thick.
I used a lot of organic matter in my garden, especially a certain section that was a silty clay. I could tell a big difference. mainly in tilth. Drainage was helped too and drainage may be where it does you a lot of good in your clay.
