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Hi Sarah. I'll be happy to help you with your question.
In reviewing what you have already tried I can see that you have done a lot to solve your difficulty. As a matter of fact, you have done almost everything I would suggest you try.
I can understand your reluctance to wear occluded glasses in public due to their extreme lack of cosmetic appeal; they are, however, a very safe and simple solution to a very complex problem. Have you ever tried just putting clear scotch tape over the right lens in your glasses? This should block the vision enough to ease your symptoms of diplopia while at the same time not being as embarrassing as a black, occluded lens. Also you could wear normal glasses but with the incorrect prescription over your right eye which would blur things enough to resolve your diplopia. This would be a lot like putting a lens inside your eye, except safer then surgery -- although, I admit, you would still be stuck wearing glasses.
So, let's get back to surgery to put a intraocular lens(IOL) in your eye. You know, of course, there are risks to this surgery, small as they might be. In thinking about this it should be possible to put the "incorrect" IOL in your eye still see the retina easily. Should you later in life decide to try restore your vision in that eye it would be possible to exchange the lens for one of the correct power -- although this could be difficult surgery with much greater risk.
When it comes to having strabismus surgery to realign your eye, before or after putting a lens inside your eye, there is a high probability that you eye will not stay straight. This is because, if the vision is not good enough to use the eye your brain doesn't work to keep it aligned for stereo vision.
I understand the difficult position you find yourself in with your diplopia. You have tried all the "easy" solutions and are still having problems. I see that you are in Australia, where I've never been but hope to visit, and I don't know any ophthalmologists well enough to recommend one who might do what you ask. I do, however, know one in Dallas Texas who would put a lens in your eye. You can contactXXX@XXXXXX.XXX om
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