Unfortunately the 29750 is fairly expensive and isn't widely available:http://octopart.com/partsearch#search/requestData&q=MIC29750&start=0
There's 400 on Digikey, but that's not really the kind of safety margin I want for part availability. Plus they're $13 each... 3x as expensive.
But the MIC29502 is the same family of part and so it can handle 16V as well; just not at 5A continuously. Also, according to the datasheet, this 5A model can actually take 7.5A briefly. That's some nice overhead there.
As for heat sinking, there's not really room for one, unless it were to be mounted on the back of the PCB. Mounting the regulator off the board isn't an option here. And besides being the size of a credit card, the board also needs to be as thin as possible. So in general, it will need to run without a heat sink. But I have put vias beneath the part to sink it to the ground plane on the opposite side of the PCB like my LED drivers, and there are mounting holes in opposite corners of the board which can be used to attach the board to whatever case they're using, and those should draw some heat away as well.