I'm told Gypsum is also a great amendment for clay soils. (We currently have clay,) It's a soluble mineral, but it somehow works to make clay act more like loam, I guess? Allows better drainage for plants to establish and get that microbiota in the soil flourishing.
Otherwise, I would think to suggest planting a few scattered trees or shrubs that do particularly good in clay, mulching well around them to help the soil be healthy, and see if that can't make a good helpful difference to the area around them. (Mulch, mulch, mulch!) If those also happen to be nitrogen fixing, that's another bonus. If you can be successful with clay-happy plants, then I'd think you would have better confidence and practices and environment with/for other plants after that.

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