In reply to Rog Wilko:
Is there any reason why you cannot try multifocal contact lenses, and get rid of the reading lens, as in good part the multifocal ones will allow you to focus at a closer distance, than the usual lenses for myopia? You could add in some cheap, less strong reading glasses if the multifocals do not do enough.
It seems to me that by continuing to use different focusing lenses, that you are continuing to create or extend the problem.
I had a major climbing head injury 17 years ago, and had a fracture of my lateral orbit, and with it I got damage to the VIth nerve, which supplies the lateral rectus muscle. So initially I had diplopia, but eventually it went away: However when I am really tired when driving long distance it comes back.
I also find that I get a strange variation when cycling for a period of time. It is something to do with looking ahead, not completely horizontally, maybe with the confusion of the moving tarmac/ground too, beneath me.