PAR lights have no business being used in a family room, unless you have a high vaulted ceiling. The beam spread is just too narrow and concentrated to be useful. You either want a BR40 or BR30 bulb, or one of the fixture/light combos, such as the CREE Cr6. They'll give you a nice wide beam pattern -- anywhere from 90 to 120 degrees. For kits, I'd go with something like this: http://www.golights.com.au/lighting/downlights/led-downlights/led-downlight-kit-alluminum-dimmable-18w-90-degree-ip44-premier-sunny-lighting Here is a led BR40 bulb: http://www.ebay.com.au/itm/Philips-423756-14-5-Watt-BR40-LED-Indoor-Flood-Light-Bulb-Dimmable-/400480586367

Based on how you're describing, I like the two rows, 3x2. This is just a personal preference thing tho. I wouldn't split them on two dimmers. I can't imagine wanting to set half the can lights on one dim level and half on another. I'd put them on one dimmer, then wire the 2nd dimmer to a couple floor half-outlets or accent lighting. Then you can run the can lights or the other lights (floor lamp) or both. I would also put them slightly farther apart than even spacing wall-light-light-wall. Otherwise it will be overly bright down the center where their beams overlap and not as bright on the fringe. With 13', I'd go something like 3.5' light to wall on each side with 6' between the two rows. That's just what I'd do.

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Have lived with much the same issue (room is 14x16, faces N, windows are on the west wall) only it’s the master bdrm. It’s like a cave until very late afternoon/evening when the sun gets closer to being below the eave on that side of the house. Electrician came to consult and will be installing 4 recessed cans on a dimmer, one in each corner. I’m still debating whether to have a fan installed (not putting on a light kit, however the wiring would be done in case I want to add one later). There is currently no ceiling light, and the existing switch is for the N wall and controls the lamps on the dresser. In your situation, given how you intend to use the room, perhaps a center fixture might be something to think about doing. When it’s no longer a playroom, a ceiling light/fan gives you an option, and it let’s you get the whole drywall repair mess done at the same time. Good luck with your project…super excited about mine! Finding someone to actually come and repair the ceiling is my current challenge.