Plastics are not as stable as metals, wood or other materials. Museums, for example, have reported that entire collections of 40's and 50's items of contemporary culture (of which, many are plastic) are literally melting. Old film stock (nitrocellulose) can become unstable as it gets brittle and crumbles. I've read old movie masters - the raw scenes as well as the original full length, edited movie have been lost, sometimes before the owners digitized them. All this is to say that modern plastics, while perhaps more stable than the early ones, still deteriorate when exposed to sunlight and weathering and there is not much we can do about it.
I'd try one of the headlight polishing kits (maybe even the toothpaste idea suggested by
@larryg) first. Then I'd consider taking the thing apart. Does J&M sell any parts? Maybe the whole enclosure with the window? That window is likely glued in and you might damage the case trying to remove it. I have no doubt that with a machine shop's tools, you could cut the window away, mill a new window to fit, and glue it in place, but the amount of work might not make any rational sense.
