hay cut in the fall is a different animal.  the fiber content is low, the plant soluble sugar percentage is very high.   Im 50 years old and have been a student of high quality square bale alfalfa hay production for 36 years and can tell you the maximum moisture content for a bale to keep well is not the same for all hay.

 course &stemmy, low rfv, late cut (blooming), rained on in the windrow and such can tolerate a little more moisture than the same hay from the same fields that were cut early, with no rain.

likewise, hay like you described baled in the fall in a dense square bale may not keep at 15 or even 14 unless the bale can continue to "breathe" in a barn.  I just pulled fourth cutting samples that were stacked in the barn late september, staggered only two bales high with 6" of space all around each bale.  the hay test came back 14.93 moisture, and yet there were hot spots in some of the bales and they were all on the verge of turning hot or not.

there is just such a concentration of plant sugars that microorganisms want to start eating, creating heat and it snowballs.   that said, square bales stacked with cover pays for itself and more. 

edit to add the sweat proccess that all hay goes through can last six weeks at least.  I usually wait to test hay until it has stabilised after the six week sweat period.