I don't think the LAA policy allows the equivalent of 3 doubles in a row to be worked whether you are part time or full time. I could be wrong though. In hubs PT does not get day off OT, but I hear in smaller stations they do. There is a 40 hour requirement before the day off OT is paid as OT and not extra straight time hours.
You are correct about doubles, but you can do 14 hours on that third day if you work a 6hr PT shift...