Lee I know the feeling - I have shot off my right shoulder for 25 years but after a break of several years, I found that my left eye was talking over. Couldn't hit a thing with my sbs, switched to OAU - a little better. Bought easyhit stick on sighter - some improvement, but not a compete success. I still find I need to shut my left eye when mounting the gun. This works, and I now do it without thinking, but it does affect depth of vision and distance judgement. Had a lesson at Fennes near Braintree and she had me shooting off the left shoulder very successfully. BUT when you know where they are coming from its much easier to mount gun etc. I think it would be more difficult with live game due to unpredictability.
So the dilemma is - stick with shooting off right shoulder, knowing I will be limited in how well I can shoot, or go for it, sell my gun, buy a leftie, get some lessons and hope that with practice I can learn to shoot better off the left than I do off the right. Stick or twist!
Personally I think switching shoulders is the only way to improve due to my strong left eye dominance. The problem is that I am not shooting badly enough to make the decision an easy one.
Back to your post - in terms of cost (1) switching to a left handed gun will cost assuming you buy a like for like replacement, actual cost will depend if you can buy privately or through trade (they need to make a margin but in return offer advice, service and wide choice). (2) some lessons - worth every penny in my opinion. Actual cost varies but 2 or 3 lessons will make a big difference. Good luck.