Also, try to reinforce the ceiling around that area. Personally, I used 2x6's. My house is newly built so I had the luxury of seeing exactly how they built the house and the HT room. They used various beams but in order to give myself the added flexibility of moving the mounting location back or forth a foot, I really needed to have the extra reinforcement so that I would always be securing the mount to solid wood and not just drywall. This is really something that you could do aolong with some help if you wish to go that route. Anyway, what I did was cut some 2x6's and use L-brackets to secure them between the beams.
Regarding the placement of 15' for the cabling, this should work well because you will have a situation something like this...
... with the cabling looping towards the projector. The 13.5' mounting distance will place you in the ballpark but before actually placing the mount, you will want to check it first against the screen for proper throw to be on the safe side.