If the park is open from 8am to midnight, then I expect you are hitting the park on a very busy day. Expect LONG lines if you don't have FPs. I just returned and FP+ our entire days at the parks. Once you are done with your 3 initial FPs you can continue to get more, one at a time.
Here is what I did.....park opened at 9am.
Pre-Selected FP
10:00 Small World
11:00 Peter Pan
12:00 7 Dwarfs
When park opened we went straight to Thunder Mountain, then Splash Mountain (both of these had less than 15 minute wait). Then we headed to Pirates (20 minute wait), Swiss family tree house, Aladdin Carpets and Tiki Room. All of these were done within 1 1/2 hours. Around 10:45 we did our FP for Small World and then went straight to PP. We then filled in the gap before 7D with the carasol and Mickeys Film harmonic (whatever that is called, little wait time). Once in the FP line for 7D I started looking for our 4th FP it was Dumbo. Once in Dumbo line I started looking for the next, it was Barnstormer. I continued this throughout the day.
If I were you, I would move your 8am FP out to something around 10 am. Leave the first couple hours of your park time free while the lines are shorter. If 7D is a must...then yes, go there first (but be prepared for crowds with that too). At rope drop there were ALOT of people with that plan when we there and that pathway was jammed up with people. If it 7D is not a must, then take those 2 hours to do the other biggies (space, thunder and splash mountains)
I would also move your 3pm FP to something at noon. This way, you can start to get your others lined up.
Fair warning - this system is great to avoid the lines. But, it does cause your face to be in your phone quite a bit while maneuvering the rest of the FPs. For best results it also good to know the layout of the park so you don't find yourself walking from one end to the other all day long.
If you decide to move around what you have now...don't be discouraged if you can't find anything to move them too. The day before your park visit and the day of is when FPs typically open up as people are adjusting their plans.