Argh, I wrote a really long reply and then it got lost. So here goes again.
DD had a really severe squint and had two operations to sort it before she started school. She still has a slight squint, but before her eye was entirely turned in.
I do understand how you feel about the consultants: we had much the same experience when her squint started to return again after the second operation and they said there was nothing else that could be done. So we ended up looking at alternatives as well.
But I wouldn't pin all your hopes on surgery. After DD's two ops, we are at about the same place you are, which is that she has a slight squint which is corrected by her glasses prescription. The hospital thought that this was a very good result, so it's not that accurate. They also refused to do the operation until patching had ensured that she was using both eyes equally. If he can't see out of his lazy eye that much, it sounds as though you are not there yet.
We have ended up doing eye exercises with her - she wears red/cyan glasses and plays 3d games on screen to encourage the eyes to work together. This has definitely helped, although progress is painfully slow, and she does now have some 3D vision, which is a great improvement.
We use a site called Engaging Eyes, which is mostly geared towards dyslexia, but DD just uses a bit of it. But it might be worth going to see a vision therapist to see what they suggest and whether exercises will help.
I have read that exercises actually work better if you haven't had the surgery. DD's squint was so extreme that there was no way she could not have had it, and I only came across the exercises a long time after that. But I would definitely look at this first.
Oh and another cheering thing, people have developed 3D vision even as an adult. So as long as he is seeing with both eyes, then they can learn to work together. DD is now 9 and her vision is still getting better.