I’ve heard of operations taking 8 hours (perhaps longer still?).
As others have said, a single 18650 would do 100lm for about 10 hours, but I can understand why a surgeon might want more than that to make absolutely certain he doesn’t get caught short. The last thing you want is a cell change at a bad moment.
Two 18650s wouldn’t be drastically bigger, but double the runtime, so you’d have time for unexpected overruns and also extra capacity for unnoticed aging of the cells reducing their capacity.
3 or 4 18650s would run for a lot longer than I’d want my surgeon to be awake 
but there could still be a use for that if the unit needed to be reused in an emergency without having had time for a full recharge.
Having the extra 18650s also helps avoid running them down to lower voltages that might cause the driver circuit to drop out of regulation.
Many people consider Nichia’s high CRI LEDs to have a more natural tint than Cree’s high CRI offerings. I’d strongly recommend trying LEDs from both manufacturers as you refine your prototype.
Some people react poorly to PWM, either because they can see the flicker and it distracts them, or because they get headaches even without consciously seeing the flicker.
I would lean towards constant current for this project. Rather than use a flashlight driver, I’d consider an adjustable constant current regulator, which would allow you the potentiometer control you want. At the likely 350mA range - or even 500mA to give a bit of leeway - even a relatively simple, linearly regulated circuit would be dissipating well under than a watt, which isn’t too bad for heatsinking, given the likely space available within a belt-mounted powerpack.
I presume this device needs to be sterilised; sealing your enclosure well enough to withstand that will take significant work. Alcohol is really good a getting round seals, for example, and will perish some rubbers and plastics. You can’t autoclave something with a Li-Ion cell in it; the 100+ °C of an autoclave drastically exceeds the 50 - 60°C maximum for a Li-Ion cell.
You might consider swappable battery packs, so that they can be permanently glued shut - no alcohol leaks - and swapped out for recharging, as long as you use a locking connector to avoid it being pulled apart by accident in use. Obviously, your connectors will have to be a type that won’t allow liquid ingress. I don’t know if it’s practical to have a battery box with a wire to a control box with another wire to the loupe-mounted light emitter?
Finally, beam profile: a beam that’s 2.5 inches diameter at 12 inches is about 12° in diameter. As Lightbringer says, you can get TIR optics going from 5° to over 60°, in clear, pebbled or frosted types to achieve all manner of beam profiles. They’re cheap enough for you to buy several types and experiment to your heart’s content.
The beam is affected by both the TIR and the LED you use, so you’d definitely need to try different combinations to make sure you got the best result. That’s no loss, though, because similar issues apply to reflectors and aspheric lenses.
Is it a problem if the beam spills some light beyond the 12° you’re looking for? You might have to set the LED / optical assembly quite deeply into a black tube if you need a sharp cutoff at the edge of the beam. A 20mm optic would need to be set inside a 90 - 100mm tube for that. It is possible to get smaller optics, though; a 10mm optic would get that down to 45 - 50mm, for example.
All in all, an interesting project!