I needed a few chunks of acrylic that were a little thicker than anything in my supply closet. Cyanoacrylate (superglue) bonds PMMA nicely, makes an optically clear joint, is easier to work with than acrylic-specific solvent glues, and doesn't add nasty internal stresses to the plastic.
On the downside, the bond isn't quite as fast (I suppose this is just as easily an upside) and the index of refraction of the glue won't be quite the same as the sheet. A perfect joint will still be noticeable right around the critical angle where seam's angle of total internal reflection will be a little different from the rest of the plastic.
IMHBCO that's small price to pay for getting perfect, strong, bubble-free joints every time without getting light-headed indoors.
Pic related: two in-progress parts curing and my go-to favorite CA glue. Once the glue is fully cured, I'll mill and polish them into rough lenses.