I'm still learning about all the technicality of batteries, LEDs, and drivers...but you could go with an taskled h6flex and set it for 2.8A or 3.6A as max or go with another driver to give you 2.8A-3.6A to hit the high 2500-2700 lumens. I would make the copper heatsink thread into the copper case with very minimal tolarance to allow maximum thermal transfer not just to the heatsink but to spread it throughout the whole flashlight casing. From there, you can machine ribs into the case to help cool things off, but for the battery, I would make a sleeve(plastic or if you can get your hands on it, ceramic) to keep heat away from the batteries. From my understanding, you would need 32650's for their higher capacity so you can have decent run times at higher lumens.
Expensive flashlight? Absolutely, but a high tech one at that plus I'm willing to bet you can get a longer continuous run time before it gets too hot to run compared to an aluminum flashlight counterpart.
But before you or anybody make a point about it being too heavy, ask yourself how many people actually carry a 2500+ lumens flashlight? I do not know very many honestly...