I think we can get one thing fixed (and that helps).
So I have a full caclulator setup now using that reference I posted. I did make it, but I didn't make the equations. I did check some of them and looking into others.
I'm not sure I agree now that 22uH is a must. I actually cannot find anything in 22uh above 12A rated (you can find higher saturation, so maybe good cooling can push one beyond spec) smaller than 22mm. I did find this comprimise: http://www.digikey.com/product-detail/en/vishay-dale/IHLP6767GZER150M11/541-1287-6-ND/ at 15uH 14A rated 17.15mm 12A saturation shielded inductor. I'm not worried about the saturation. At high current you can live with less inductance. This might be the part. (darn expensive though)
But I think we need smaller than 22mm. Basically everything above 10uH above 12A, shielded, below 22mm is 17.15 *17.15 or close enough to not matter. So I would say that is the footprint. What do you think? There are options here. You can get a 19A 10Uh if you want high power or a 12A 22uH if you want better low power efficiency, so the end user can decide.
Now as for 10uH, Plugging some numbers through my calculator, at 10uH you get 2 to 4% inductor ripple current at high power (15A) at 1MHz or 8 to 15% at 300 khz, but lowside cap of 10 or 20uF easily shields the output voltage from this. The problem is in low power, 0.25A per LED you start to get in the the neighborhood of 100 to 300% ripple current or more in 2S depending on frequency (200 means entering discontinuous mode I believe), 3 times less still in 1S. But that's not the end of the world. Ok, so at low power you enter discontinuous mode. We know that and have discussed how to deal with it. I'm still only getting 7% total power loss (my gut says it will be twice that from realities not calculated, edit: gut was right, had an error in inductor loss equation.) at the threshold to DCM. The question is how low and at what frequency? From the equations there I'm not seeing big switching losses, but I want to review that more. 1Mhz makes me concerned we'll see unpredictable losses from many parasitics we can't easily predict, but this probably isn't a footprint issue anyway.
As for the diode it does look like it will be the biggest loss (edit: in some situations), but it's ok and hardly an issue at all in 4S to 2S.
I'm not worried about 4p personally. Rewiring the LED board is simple, but I see your point.