By the way, the same shade was not indicated, maybe it makes sense to contact those who make custom budget lights? Then can put a suitable driver, the body on 4 * 20700 and 3*n diodes with a temperature of 7-8 kk for greater efficiency?
. . . . . . you are thinking only in mah not in voltage. a 6000 mah cell is about equal to 2 18650 cells in watt hours, 23 watt hours vs 23 watt hours. still shy of nessicary and only 1 26650 can do it and it's 28 dollars. some 18650 can exceed that performance with 14 watt hours, times 2, or 28 watt hours. If Nitecore tried to or you rebuilt their light the tm10k should be able to have 3 hours at 1000 lumens but would no longer have a 10k lumen max killing the namesake. now, a 3 18650 makes sense, or even perhaps for space a 3 18500 light would be very compact.Obviously larger cells like 26650 have more capacity and better than that 2P 18650 or even 4P 18650
I agree completely - beam pattern is important to identify up front. What is the intended purpose of the light? As others have said you are not likely to notice the difference between a true 800 lumen light and a true 1000 lumen light, but if the beam pattern (flood versus spot, smoothness of transition, etc.) is not what you need that will become a problem real quick.
You have not announced the budget and the required coverage range - close or long distance?
I doubt the OP has read any of the replies..