It is my understanding (not a pro, but had vision problems myself and know the CAA guidance material rather well) that diplopia is an automatic disqualification.
BUT, do not give up hope. Look into your options with private opthamologists and see what can be corrected. It may not be good news, but you never know until you try.
I've spent the last 16 years without a medical because I gave up when I didn't think I could meet the requirements. Turns out I was wrong, I just needed the right optometrist and spend a few months of patience whilst getting used to contact lenses!