Ouch, that's too bad. Spindler plastic strikes again :sadmac:
I've gotten to the point that I try and handle just about anything Apple from the mid-late 90s (5xxx, anything Outrigger (72/73/75/76xx, Beige G3 DT), and 85/95xx) as little as possible. Back when I had a Performa 5200 it made some very worrying creaks just adjusting the tilt, to say nothing of picking it up where it felt like the case was flexing.
Given that the cracks and missing plastic appear to be at or very near the CRT's mounting points I wonder if it would make any difference to handle them with the glass facing down. Meaning instead of carrying it like a normal monitor by holding on to the sides with the glass facing back towards you, carrying it by holding the sides of the front bezel with the glass facing down.