Not 7135, now you're following my mispeaks. If a 7135 reduces current from the buck, then it reduces current out of the buck and the buck has to operate at low current, and we're current regulating it anyway. You've only raised the output voltage slightly, still with the same current, and dumping the extra dVI into resistive loss while not improving anything.
But I made the same slip on the last page. What you mean to say is for lower current you do LED PWM. That needs and extra FET, but not a big one because you start with low current. This was brought up by a couple of people in the "more efficient driver" thread.
Anyway, the cap I was talking about was input to the FET, parallel to the source. In principle that does nothing since it's hard tied to the source (and the batteries probably have pretty enourmous capacitance themselves) but this note mentioned stray inductance and needing this cap very close to the FET because of that. The claimed effect was very impressive. I lost track of the link. I'll try to find it again.
I started (not completed yet) my own calculator based mostly on this:
http://powerelectronics.com/site-files/powerelectronics.com/files/archive/powerelectronics.com/mag/606PET25.pdf
A very practical summary of many of the basics. It's probably redundant with your spreadsheet but I'll compare later.
Anyway started looking at inductors. It seems to me there's quite a bit in 22mm * 22mm * 22uH. My initial impression is that 22uH would be nice, but size is still a pretty big problem there. It looks like you've started with a bit smaller footprint, which is probably sensible if it can work. Going shielded certainly takes more space. Aparently shielding above 200khz can be conductive shielding (thin metal, maybe tape) and I don't think you need that much space to get away from the fields. The irony is by requiring shielding you force things well up over 200khz anyway likely by not being able to get as much inductance. An open inductor with shielding tape, maybe extra added, at 300 to 500 khz might not be a bad way to go.
Anyway, I've only just started looking, and just started seeing how actual numbers fit in the math. Math aside I've seen 22uH actually used in a cheap 10W driver. So it's not an absurd number, maybe just absurd for 15A. I've noticed though that some of these inductors, like Vishay can keep going well above their saturation current. They just don't go as well, so things will get more wild and less efficient, but this is pushing up into turbo modes anyway, so so what.
12A (plus ripple) will run 2S 2P at 6A per diode. That's already a BUNCH. And it will run 4p at 3A per diode which is also plenty high really and you can still crank higher with some slop and heat. I've been aiming for 15 saturation so far, but it's probably higher than needed. This is why I would buck a Q8 at 4s batt 2s LED. It's the only way that makes sense to me. Many factors to trade off though.