I've done lots of polishing of fibre-optic connectors. I have some idea what I'm doing. Go and buy some new glasses, or lenses for the current pair. Get your prescription checked as you do, unless it's been done recently. No point getting new lenses if they're wrong.

If those scraches in your glasses are of any size at all, it will be nigh on impossible to remove them at home. Trying to get down to a acceptable optical finish with the abrasives and tools designed for the job is quite hard, even with some practice, and that's on a circle one two-hundredth of an inch across ( 125 microns). Doing so with improptu stuff, on a much larger area could be a fun job. I'm not saying don't try, but regard it as a project, to gain a spare pair or glasses, not fixing your only pair.