A couple of feet down isn't really going to make a huge difference on the posts, imo. You also have to think about the structural integrity, or the lack thereof, if you have all of them dug up at one time to pour the concrete. I honestly don't think you will be disappointed if you just pour a concrete slab floor within the perimeter. How thick are you wanting this floor to be? What strength(psi) concrete are you looking at using? Steel rebar?