We took some photos of his lifeless body and noticed that he (or she, or it) had some egg sacs, we didn't see him lay any eggs, but it's possible. So we're going to let the tank dry out. (The eggs need to be dry before hatching) So far, the tank hasn't been drying very fast, but we've moved it to a warmer place which will hopefully work.
The top two photos show his egg sacs that are filled with eggs. The bottom left is his underside, and the bottom right is a close-up of his tail.
Some more parts of the triops. The upper left photo shows the algae on his shell, the photo on the right is his back legs, and the bottom two show his eyes.