"here" 2 feet is the minumum, and it's a heck of a lot dryer here than where you are. Both in surface water and the amount of rain/snow than you get.

I've seen guys stack hay on 2' shale inside a barn and still get moisture damage 'here'. 

It really depends on what is acceptable for spoilage loss in your situation.

'Here' where a bale of hay is worth $10-$16+/bale, and even a yellow tint on a bottom bale gets it rejected, loss can add up real fast. (3 twine bales)

Straw is the best 'sponge' ever devised, even worse than grass hay.

Obviously choice is yours, and if you get the floor all done and a year later start removing the bottoms and find damaged hay it's going to be un-fun to fix the floor then. The other thing to remember is if you use the barn to store heavy machinery and you have cement or asphalt,, that is going to be alot of weight on a relatively very small area, and the machinery will be setting there awhile.  You don't want the floor sagging, or getting divots in it, or cracking. Likewise if you're stacking clear to the roof, hay is pretty heavy.

"Here" even sun bleached hay is an awful reduction in price, minus $30/ton isn't uncommon. (I've had some buyers flat refuse to buy sun bleached hay)

Barn will be there 40-50 years right?  (with barns-pipelines-etc, I always consider long term. What would be the total cost difference between 6 inches and 3 feet over 40-50 years?)

Neighbor built his barn himself, used the hay pile itself as a platform for putting up the trusses and roofing.  Few years of losing bottoms from moisture damage, (just gravel floor) he decided to put in a cement floor. After measuring,, he discovered his barn was "too short" so he had to go in dig out 1foot of gravel, then dig down another 2.5 feet and rock it back in, then gravel-plastic-gravel-cement. As is now, barn floor is dry, but,, at ground level, so in the winter time he really has to stay on top of snow removal to keep snow/water from running down into barn.  (he built his barn in the lowest spot he had...)

Just trying to save you some serious grief in 2-4 years.