I am certainly not an expert woodworking teacher, but I have a lot of experience teaching folks to shoot. Eye dominance can cause issues in shooting, just as you are experiencing problems sawing. I think the fix used in shooting could work for you.
When I was taught to saw, I was told to sight down the plate with my dominant eye to keep the saw at a right angle to the work and sawing to the line. I’m right handed, right-eye dominant, so that’s what I do. That simple act could well be impossible for folks with an eye dominance issue. One would have to contort the body to the point of ruined saw technique to get one’s dominant eye behind the saw.
Luckily, there’s a simple solution. Close your dominant eye and use your non-dominant eye to sight along the saw plate. This is the same solution used when learning to shoot a gun while suffering the same type of eye dominance issue. A shooter can sometimes turn their head to use their dominant eye when shooting a handgun, but they cannot do so when shooting a long gun. Thus, they have to either switch to their non-dominant side to shoot so they can use their dominant eye, or learn to use their non-dominant eye behind the sights. I think you may be in the same boat.
It may feel quite odd to shut one eye, particularly your dominant eye, while sawing, but you can get used to it. Your other option would be to learn to saw left-handed….I think for most of us, keeping the saw in our dominant hand would yield much better results.
Just my two cents – hope it helps you.