First, let me categorically state I'm no prop expert. My knowledge comes from experience (R/C planes & MCs) and some research.
Second, you should plug the appropriate information into eCalc (
http://www.ecalc.ch/xcoptercalc_e.htm?ecalc) as a guide.
Third, your calculation is "the maximum" condition. Unlikely you'll be flying at full throttle.
Fourth, a lot of this information is "recommended" and should be used as a guide; not necessarily as hard & fast rules.
Fifth, make sure there's a corresponding "pusher" prop for the tractor prop you want to use. Many of the APC props do not have a matching (dia., pitch, & style) pusher prop.
Finally. I flew my hexa for a while on 3S batteries and APC 12x3.8SF props. It flew fine until I put more payload (i.e., heavier camera) on it, so I moved up to 12x6E props. That helped, but I needed more, so I went to 4S batteries. Now it's perfect. You may have to experiment with a fe sizes to get it right for your configuration.
Jack