Just a quick update.
I screwed two pieces together without using Loctite; these were sections of a broken piece that weren't subjected to Loctite prior; basically pieces I plan to throw away.
First I tightened the screw to where it caught. Basically this was loose enough that it would probably unscrew with the slightest vibration.
Next I tightened the screw with approximately the same amount of torque used when I applied Loctite the first time.
After I went quite tight, and finally tighter than I would normally go to really stress the acrylic. In all cases I waited at least one day between tightening the screw more, and, although I haven't checked it today, as of yesterday, I didn't see any cracking. Also, I tried stressing the piece a bit by gently bending it and this also didn't cause any cracking.
These tests was to check how tight to safely make the screws, and whether the acrylic is really brittle. It seems the Loctite does quite a bit of harm to the acrylic because before when using the Loctite, I hadn't tightened the screws tight, and I applied just a bit of pressure on the frame. The piece literally crumbled into tiny grains with the slightest force on the frame.
Without using Loctite, I can tighten the screws tighter than before, apply bending force, and the acrylic holds up.