Here's my take on it. If you are only going to AK one day for your trip and you must do FoP without a FP, are you willing to risk not getting on at all or wait the long hours?
As some have stated, late at night it "may" be 30 minutes. Waiting until close to park close to find out you won't be able to ride is a risk you have to be willing to accept. Going at rope drop has 2 strategies that can be followed. First, you can get there early (60-90 minutes) and be at or near the front of the pack. What this allows is getting off the ride first to get to other attractions before lines get long. Second, get to the park closer to opening, wait about 60-90 minutes to get on. The disadvantage here is that you are waiting in a long line while the other attractions lines are getting longer.
Personally, we prefer to wait at park opening. Sometimes the park opens early, sometimes it doesn't. This past Summer, Park opening was at 8AM. We were there at 6:30AM, near the front, and off the ride before 8AM. The second time we went, the park opened on time and we were at the front and off at 7:30AM (7AM park opening).
The strategy you use really depends on how your family operates.