Barely adequate, especially if you are only running at 350mA. When I talk heatsink, I mean
HEATSINK. I have used these guys on a number of projects with great success. Sure they are overkill, but it will support whatever size array you could want. Using the heatsink as the base of the fixture, you could skin the outside with acrylic or wood. If you are going to run everything at ~350mA, you could run a heatsink of this size passively.
After looking at your layout pictures (which was difficult), I think you have used the wrong angle in your lens approximation. The Fraen lenses are 25 degrees total output, not 25 degrees half angle. It looks like you have a 50 degree cone in your plans.
It does seem like 15 LEDs might do it. 18 would get a slightly better overlap, but might not be needed. One reason I was saying to stay away from the 25 degree lenses is the very high PAR levels you will hit, even while only running at 350mA. A wider angle lens will lessen it and get you back to a level that is still sensible for a high light setup.
From what I have seen, there is a slightly better selection of wide angle lenses for Cree LEDs over Luxeon. Don't know if you are sold on Luxeon or not, but I know a good place to get Crees for a good price and optics too.