To detect the blocked laser beam, I decided to use photoresistors. I debated using faster components, but, after watching this great Backyard Amusement video, realized that photoresistors would work fine given my requirements.
Even with the kinematic laser mounts, I knew that I wanted to add diffusers to make sure light fully illuminated the photoresistors. I used old 35mm film canisters cut to fit in a small mount, a trick I learned from my first laser harp.
A photoresistor is pushed into the photoresistor "wall," and two cables are connected to the photoresistor (one goes to 5V and the other goes to an analog input on the Arduino Mega). The film canister plastic slides into wooden mounts and is placed into a cross-shaped part. It looks like a little lantern. The body is pressed into the photoresistor wall. Finally, the photoresistor wall is used to connect the kinematic laser mount assembly. If the laser is aligned with the photoresistor, then a low signal out of the photoresistor corresponds to a blocked laser. The Arduino Mega is cued to play a note.