I second calling AEA about this. The SF Bay has their own Staged Reading Guidelines, and we are allowed to work under those (without a formal contract) as long as the combined rehearsal and performance hours do not exceed 20. If it is planned to exceed that limit, or we break another guideline on the list, we have to be under a Periodic Performance Contract. That's just the Bay Area (and my experiences), and you won't find that contract on the website either.
If you are going beyond your area's Reading Guidelines, then you need to call AEA and let them know which guideline is being broken so that they can get the proper contract started (which may be this mysterious Staged Reading Contract). For me, the PP references another contract that the theater is usually under, which for me has always been a LORT or a BAT. Generally a new hourly wage is set, with a minimum requirement of AEA actors and a new hour limit on the project.
Don't be afraid to call AEA. My last reading that I worked on had to shift to a PP contract at the last minute because there was a ticket price charged for the event. I didn't even know we had a ticket price until I did some googling of the project to learn more about the author of our piece. That was my red flag, and I spoke with the producer, and I convinced her to be the one to call equity to get it worked out. (And she did.)
Corrected myself in the first paragraph for clarity.