Thank you all for the excellent information and opinions! In particular, the info shared by cooltouch and fin looks to be extremely useful.
I've just tried cleaning an old scratched and battered one using IPA and dish soap/distilled water.
I assume you mean isopropyl alcohol and not India pale ale!
I've just tried cleaning an old scratched and battered one using IPA and dish soap/distilled water. The IPA seemed to leave marks/streaks both on the glass and the focussing screen despite several attempts.
Soaking it in a film pot with warm water and soap, then rinsing in distilled water got it clean. Then I polished the glass and used an air duster on the screen. That seemed to get it as clean as I've ever seen this one!
Like yours, my screens are framed in anodized aluminum with flat-head fasteners. I have not attempted to take them apart yet as I was waiting to see what people's responses were here. Once I take one apart I'll be able to determine whether the fresnel is simply placed against the plano-convex screen and held in place by the frame or whether it is bonded somehow. If they are separate, then everything will be easier and I'll be able to clean each piece on it's own without having to worry about trapping crud in between.
What I may do is try removing the goo from the boxes before attempting removal from the screens. The boxes are plastic - most likely polycarbonate - and are just as gooey as the screens are. If I can clean the boxes without harming them it may give me clues as to which method will not harm the screens. I don't know why this didn't occur to me earlier.
Everyone's input has been very helpful. Hopefully I'll have time this weekend to do some experimenting.