Just an FYI, our family (as well as other friends who have done this) have had no trouble getting a FP for Tomorrowland Speedway in the afternoon and evening. And typically, there have been FP's available almost immediately when checking at the kiosk. We had a party of 5 and when I went to the kiosk to get our 4th FP at about 1:00 on an afternoon in June (crowd level 8-9), there was *a lot* of availability. I didn't schedule it at that point but did get a FP later that evening for immediate use.
Just thought I'd mention that in case you'll be spending the day at MK and would rather do something different at rope drop. If you have your FP's scheduled at a different park that day, my information won't be much help.