One trick we learned this trip - when looking for FP+ beyond the 1st 3, if the ride you want doesn't show up, put in a specific time - like 3:30. We had the options change when we'd enter a specific time - and we were booking for 12 so you can find some good ones! On our last day, we used our 1st 3 passes at Epcot, then went to Magic Kingdom. We got 6 more FP throughout the day/evening. Our time for Jungle Cruise was rained out so we got an email giving us "anywhere" passes - they were good on any ride so we used them on Space Mountain. If it's raining, be sure to check your email if your ride is closed during your window!
Yep, you can try doing that.
We're here now, and we also are go with the flow people anyway. When it comes to 4th or more FP+, we go with what's available. There are certain rides that are generally easier to get than others, and certain rides that may be easy to get on without a FP+ anyway. Even popular rides often get short lines near park closing, so if you know you'll be in the park late, you can use that strategy too and not worry about FP+ for that ride. We've only been here a few days, and a few examples for us already:
Yesterday, we were in Epcot for the morning. Had FP+ starting around 9:30am. First was TT. We had used all 3 of them well before lunch. So while we were eating, I was playing around with
MDE some. I booked Living w/the Land because we were eating right there anyway. The line was 30 minutes long (I'd never seen that before, but whatever), so since we were there, why not. However, I played around a little more while we were eating, by selecting a specific time and suddenly TT showed up for 1:15pm. Guess maybe someone dropped theirs, who knows. Woohoo!!
Saturday night, the kids were with the babysitter (walking around HS). DW and I went to the Boardwalk, rented a surrey bike (awesome fun BTW) and then went back to HS. Went to ride TSMM at 9:10pm (park closed at 9:30pm). We were second in line, waited 30 seconds. Got off, circled around and got right back on. This time we were literally the only people in line.