Thanks! After some fiddling around, I got it, and fixed another little problem I didn't know existed. FYI here's what I did:
1. unscrewed and removed the back panel
2. peeled back the 2 overlapping protective film pieces (slowly, tried not to rip the adhesive tape. Wasn't 100% successful but close)
3. used tweezers to gently pull up the battery terminal clips
4. there were 3 little square bumper type things sitting on little plastic posts on each corner of the LCD area, so I used tweezers to carefully remove them and set them aside - this is the problem I found that I wasn't aware of - there was a 4th bumper sitting loose, which had caused the gap to form originally between the LCD and the plastic screen allowing the original gunk to end up there. Clearly these bumpers are used to gently press the LCD screen against the outer plastic window once you reassemble since the back panel has extensions which fit right over those bumpers - sort of a female version of the post. The LCD circuit board is attached via a flexible piece on the right side, and is not directly/rigidly attached to the rest of the electronics - this is what allowed me to easily accomplish the next step:
4. with the LCD basically free (although still attached at the right side), I gently pulled up the left side, letting a little gap form between the LCD and the outer screen. then I picked the whole thing up, rotated it backwards, let gravity hold the gap, and reached in with the tweezers and gently touched the gunk which came right out
5. reassembled
Good as new! (well, as new as a 25 year old calculator can be). As I mentioned, those 4 little square bumpers are now back around the LCD, so now there is a nice tight "seal" between the LCD and the outer window.
