I have not really had much of a choice on the times available for my meals. We are a party of 5, so that makes a difference....its always harder for a party larger than 4...but I have never experienced this little flexibility as far as dining times before.
I just realized I had Le Cellier booked for a night that Epcot is likely to be very crowded and rebooked it (we're the second week after Labor Day). I wasn't able to get the night I wanted, but could get another night that worked better than the first. The only time available for my party either night was 8:50...late. Oh, I could have gotten 2 tables....but as we are a party of 2 adults and 3 kids I don't know if that would work....LOL...maybe I should try to get that one and just put the big kids at a separate table!
I still want the other night...so I may try to call back every so often between then and now to see if someone cancels...right up until the day of the reservation (the day I want is 2 days later). I'm not sure of any other way I could do this. I dislike having to call so often, but my plans are perfect except for this!
Good luck! If you're not picky we've always had pretty good luck with walk up seating....but mostly at Nine Dragons.