I think from a practical perspective, you might be better off using a full frame camera which will allow you to use a less wide angle lens to get the same angle of view with less of what you are perceiving (and I agree) as distortion.
I understand the technical arguments here and they are probably technically correct.
However I also get that to you the images don't look right. Because a 23mm lenses feels distorted where a 35mm lens would feel more "normal" and less distorted.
This bugs me about APS-C and smaller also.