I actually live in Montréal, so our doctor is certainly not available for you, but here is my experience anyway.
We noticed that our daughter's eyes crossed in during her first few months of life. We brought it to our ped.'s attention at the 6 mo visit and he made some calls to get us in with the opthamologist (pediatric). That took a while. We did patching from 10 mo- 17 mo, when the surgery was. The patching definitely helped strengthen one eye, which she had been barely using. She didn't mind the patch much. (Now that she is almost 2, we can't get her to wear the patch (see later).)
The surgery was to decrease the range of motion of the muscles that pull inward on both eyes. They had measured the angle of how crossed the eyes were, so they knew where to reattach the muscles. My husband had to be out of town for the surgery and my mom was able to be with me. Everything was fine in the waiting rooms and my daughter was even fine being held by the docs that were going to work on her. I was looking down signing something when they walked away with her and I looked up and saw she was gone (happily and calmly in some nurse's arms) and I burst into tears. They asked if I wanted her back to say goodbye but I knew I shouldn't do that. So that was hard on me, but I was able to be calm once I distracted myself.
They pull back the convuntiva (clear covering over the eyes) to access the muscles, so these were dark with blood on the inner corners of her eyes. She was groggy coming out of the aneasthetic, and serious, not herself. Once she was up for a while, they let us leave, and within 30 minutes, my daughter was climbing all over the place and playing like normal back at home.
The surgery made a major difference in the angle between her eyes. Everyone said so when they saw her. We were supposed to keep patching a little but we never did because the summer of her being 18-21 months was so tough just trying to be parents of a regular precocious terrible-twos kid.
We recently had a checkup (when my daughter was 22.5 mo) and they found that now one of her eyes points higher than the other, and she still doesn't use them at the same time. Instead, she alternates rapidly. It's obvious now that they pointed it out. The difference in vertical position was impossible to tell before the surgery because the eyes were so crossed in, so they didn't know to fix that.
There are glasses waiting for us now that have a mild prescription to correct mild farsightedness, and something to deal with this vertical issue. We have to pick them up and then figure out how to get this energetic, strong-willed little girl to wear them.
The hope is that the glasses will help her truly use both eyes at once (have binocular vision).
As for finding the miracle doctor, of course that is not possible because doctors practice science, not miracles. That said, we did have a visit with some interns or students or something who had terrible bedside manner and couldn't get a measurement of anything without major struggles and screaming from my baby. Our first appointment (at the same department) with our surgeon and the orthoptists went so much smoother. You'll be able to judge the competency of the docs just by whether things go smoothly and you and your daughter are at ease. Good luck and feel free to write if you think I could answer more questions.