I purchased this flashlight a few days ago, and started to measure its run-time curves since then.
I tested this flashlight with the following batteries:
ACEBEAM 21700 5100mAh: A protected battery that came with EC65. I suspect this should be a Samsung INR21700-50E. The internal resistance measured is 30.7mΩ (with YR1030). 5017mAh/17.922Wh is obtained after 1A discharged down to 2.5V.
Samsung INR21700-48G: The internal resistance measured is 15.32mΩ. 4758mAh/16.863Wh is obtained after 1A discharged down to 2.5V. HKJ's review can be found here.
LISHEN LR2170SA: LISHEN is a known li-ion manufacturer from China, and this cell is a good one. LiitoKala also sells the re-wrap of this cell. The internal resistance measured is 14.61mΩ. 4056mAh/14.858Wh is obtained after 1A discharged down to 2.5V. HKJ's review can be found here
ACEBEAM 18650 3100mAh: A protected battery that came with my ACEBEAM H15. I suspect this should be a Samsung INR18650-30Q. The internal resistance measured is 23.4mΩ. 2972mAh/10.677Wh is obtained after 1A discharged down to 2.5V.
NOTE: the lumen numbers mentioned below are rough estimations, and by no means should be considered as accurate.
First, I tested the EC65 Turbo mode with these batteries.
The LISHEN battery can sustain the ~3700 lumen Turbo until the thermal step-down kicks-in, while the other three cannot. All the other three batteries can only sustain ~3700 lumens for less than 25 seconds then the output will drop to ~3100 lumens. Then the maximum output you can get at Turbo mode will be ~3100 lumens or less, even after cooling down the flashlight.
Then I conducted more extended experiments on Turbo mode. I repeated the following process to measure the approximated output curve of Turbo.
Turn on EC65 at Turbo.
Turn off EC65 when the thermal stepdown kicks-in.
Apply cooling to EC65 (with two fans, for at least 5 minutes).

Some findings from this result:
The Turbo mode of EC65 will decrease its output in accordance with the battery voltage. ~3700 lumens → ~3100 lumens → ~2700 lumens → ~2300 lumens.
The three batteries (ACEBEAM 21700 5100mAh, Samsung INR21700-48G, ACEBEAM 18650 3100mAh) can only sustain ~3700 lumens for a very short period. So with these batteries you'd better consider EC65 as a 3000~3100 lumen flashlight.
When conducting this experiment with the LISHEN LR2170SA battery, EC65 stopped working after several seconds and turned out to be dead after I cooled EC65 for the first time then started the 2nd round of Turbo.
It looks like something within EC65 (some circuit component?) cannot afford the ~3700 lumen load for a longer period, so when a more powerful (high-drain) battery is given, this vulnerability is exposed. I guess this problem is more easily to be found if tested with a even more powerful 21700 battery, for example, Samsung INR21700-40T and INR21700-30T.
I plan to report this problem to ACEBEAM. Before ACEBEAM solve this problem, you'd better not use a true high drain battery with EC65.
EDIT: I received a new EC65 from ACEBEAM. The new test results are as follows.
This new EC65 is able to sustain the extended Turbo test and performs noticeably better than the dead one. The highest output is now fairly close to 4000 lumens (~4100 lumens @0s, ~3900 lumens @30s). This number is no longer a single burst, it can last for ~3.5 minutes with the included 21700 battery. And, the new EC65 is more efficient as well.
It's good to see ACEBEAM fix this problem quickly, I'm impressed!