If you want to develop that hard clay soil, find some feed turnip seeds. They will do the same as dandelion roots, but deeper and more mass.I genuinely don't care lol and I'm planning on using them as food/meds too so its fine. Plus I need stuff that will break up the crazy compacted dead clay "soil" in our little 18'x23' yard. Dry and dusty and definitely not primed for growing *anything* but with their mineral mining tap roots and dynamic accumulation I will leave whatever I don't use to chop and drop and compost in place over the winter as a soil conditioner and to add organic materials back in. I've been doing a bunch of research into that along with various hormones and enzymes and such produced by various types of plants and how the natural "weed" cycle goes about repairing soil structure and mineral contents and such. Every single "weed" people try to eradicate serves a purpose in the health and stability of the soil structure, pH, organic material content, etc. Pretty fascinating stuff when you get deeper into the rabbit hole.
Another alternative is L-bon Rye. I used the rye as a mother crop to protect the vetch I planted. as a part of my winter cover crop and soil building. The vetch is mainly for fixing nitrogen and a little bulk carbon. The rye is mainly for the root bulk structure and deep mineral mining. I let it grow the next spring and cut it before the rye is viable. I just cut and condition and lay in place with a hay harvester. Big thick ready made mulch layer. By the time it was ready to plant the next winter cover crop, all it took was a discing for a new seed bed.
You could plant ya a little square and harvest the greenage for a part of FPJ many times during the growing season.