Cross Dominance Problem

I'm a relitavely experianced archer (just over 2 years) who has discovered that I am cross dominant with right hand dominance and left eye. Up until now I have always shot with my left eye closed but I know this is wrong. I have tried to pull back a left handed bow out of interest to see if switching was viable but it was incredably difficult to do and felt very unnatural. Also, if I wanted to switch, all my current equiptment would become redundant, which I would preffer to avoid.

Is switching hand really the only way to fix this issue or is it possible to train the other eye to work better? I know actual dominance is hardwired but i wandered if it was possible to train a kind of ambidextrus ability.