Yeah, that “shadowing” on an active matrix display is a classic symptom of bad caps. That display should be 100% fine once recapped. Another symptom sometimes is the display looking washed-out until the unit warms up (I have seen this on some old Compaqs before).
Cost would be insane, but if they ever set it up for research like the National Archives, that would be wonderful. Might the Woz be contacted to fund such an endeavor? It would be very sad to see so much technical history molder away in storage un-scanned.