Yes the first period will be busier, its more in the middle of the month and popular fall break time espically around Columbus Day. That is also why WDW has blacked it out from Free dining. The expected crowds levels and resort occupancy rate are at a level they are happy with so they didn't offer a 'deal' during that time.
I would also check into rooms, as PP said they are limited but I'm not sure what's going on with the dates PP checked I just checked for a client yesterday and found some stuff in that range for free dining. @MickeyFliers did you look under promo rates or just rack rates?