I have claypan problem each summer. Only way I found was to deep dig the whole garden with sharp spade each autumn and leave it to freeze during winter (which judging by your flag is mission impossible
) and then from spring to autumn dig with hoe every 2 weeks and after every rain. As for waterlogging collect the water away from the plants, surround each bed with small canals for the water to drain as far as possible. I live on a hill so I have natural draining but my grandma had fields that were in the bottom of a hill and were flooded every year and she always had canals between each row of plants. Something like this.
In big fields rotovator definitely works wonderfully, but once you've planted something it's hoe time