If you can remove the secondary and the secondary housing from the corrector plate you then have a whole heap more options available, as a lot of products might etch the metal but not harm the glass or coatings. I've never owned one of those so don't know if it separates down to just the glass corrector plate.
If you can separate the components your best option is a chlorine based pre wash soaker. You will need to leave it soak several days. Let it soak for 24 hours then rinse off any crud that has loosened and put it back in the soaker. Continually repeat the process, it will work deeper and deeper over several days as you rinse off the top layers.
The same stuff also does a really good job of cleaning glasses and other kitchen items that have become grotty. I know it sounds silly but trust me on it. I worked in hospitality for 30 years and we used specialised chlorine based soakers (Bracton Pink) to clean all the glasses, crockery and cutlery. The stronger pre wash soakers are chemically very similar to Bracton Pink, except they aren't pink.
Sards Super Soaker at Woolworths