The treatment for clay soil is the same as for sandy soil: add lots of organic matter. What do you have that you can add to your soil? Wood chips, leaves, chopped straw?I was curious to ask what soil ratios you tried other variations of possibly some sand with the soil for growing potatoes also? And how they'd turn out? And what's the limit of how much sand you have to have to keep the potatoes from getting glued into clay? Where I'm at we have terrible clay soil, that makes it hard for the potato plants to not get glued in from.
I have a garden that is very heavy clay, and one that is very sandy. I haven't tried to grow root/tuber crops in the clay, so I can't advise on that. I have been adding wood chips and other mulch as much as I can, as much as I have. I can definitely see an improvement.
People have grown potatoes under piles of straw. I've never done this, just read about it.