IF it works as it did when we were there 6/13-20, you should be able to do this. Personally, I'd still keep the SDMT FP just to be able to ride it a second time.
It really doesn't matter that you have an 8:20 adr- they will let you in the park at the same time they do the 8am adr and BOG will seat you. You should have the same advantage as those with earlier adr's. We had an 8:10 adr. We pre-ordered our meals to save time and even with a slow eating toddler, were done shortly after 8:30. We were not first in line where they hold you for SDMT, but we had no trouble getting in on the first ride of the day. We could've easily ridden those rides twice. I would definitely make PPF my first ride after SDMT, then head over to the mountains.
In September you should be looking at lighter crowds than we had and this would've been easy to do for us.
I think the key is to to get the MK early- we were there around 7:15 and there were a dozen or so people in front of us. By the time they let us in around 7:50, the line waiting to go in was very long, probably 100 or more people. This includes more than just BOG, but the further back you are in line, the more crowded the restaurant will be and the longer your meal will take. We were able to stop and have photos taken and enjoy the walk and still had a light crowd at BOG when we got there.