3" of asphalt (top coat material, not base layer of material) on top of 10-12" of 21AA, all setting on subsoil (removed top soil first), have natural drainage away from 3 sides (one end is basically level with floor, 2" drop). My asphalt was laid in two courses (lifts?), basically 1 1/2" finished layer at time. I was told compaction is what is important, with asphalt.
All bales stored on edge (un-cut side down), on 80' of asphalt. The last 40' of my shed is 6" concrete floor, this is were I try to concentrate traffic (especially turning).
Bales stack directly on asphalt, zero mold problems, placed a layer of straw bales under hay (thank goodness) that were temporarily stacked on concrete, within a week straw bales had mold on bottom. As did 3 hay bales that I placed on concrete just to check for myself. 
BTW, the 6" of concrete had 10-12" of sand put down after topsoil removed.
The asphalt guy, told me asphalt doesn't cure, but cools. Comes out of the plant at over 350 degrees, being it is made of petroleum based products, there is evaporation. BUT I should see minimal evaporation, being my floor is not in the direct sunlight (he claims asphalt can re-heat in direct sunshine in the summer to over 150 degrees, here in Michigan). I should never need to coat my floor with anything, for this reason (lack of evaporation), for a long, long time.
Leaving impressions/marks in the asphalt with tractor tires does happen, hasn't been a problem since colder weather has arrived here. I don't have a skid steer, just tractors and telehandler (being the telehandler is the heaviest at over 18,000#, you can guess what leaves impressions the fastest). I chose to go the telehandler route, because I didn't want to tear up my hay fields with skid steer (I use a 15 bale accumulator/grapple system).
I was also told that turning on asphalt tears it up, so I try to have equipment (tire) turning/moving would help reduce this situation. Seems people have a tendency to turn the steering wheel while vehicle is stationary.
One of the 'do overs' at this time, would be I would have used crushed lime stone that my asphalt guy recommended instead of 21 AA. His told me this after I had the 21AA delivered/rough graded. I would have saved a few coins, even.
The second 'do over', would be 72' wide (instead of 64'). It's surprising how much room it takes to turn stuff around. 
Lastly, my asphalt guy is also a local beef cattle/hay farmer. Knowing that everything he told me could be questionable at best. 
I got a lot of good info from the great folks here on HT, their advice/opinions are invaluable. 
What sold me the most on asphalt, is here in Michigan, with a concrete block (or pour wall), they always 'coat' the outside with tar to stop moisture migration. I believe tar and asphalt are both petroleum products (even possibly closely related).
HTH
Larry