Just cutting a hole won't help necessarily. You need to create airflow. Small hole in the front, a second hole 1.5 times as large in the rear for an exit. This is to facilitate the expansion of the hot air.

A larger ESC won't solve your problem if this is a LVC cutoff issue. The bigger ESC will still cut off because the draw on the batteries is the same, and they will still suffer the same voltage depression.

There's nothing saying here that you didn't get a dud cell or pack. Unlikely, but not unheard of.

If you could do a Whattmeter pull on each of the three batteries, just to see what happens, that would tell us pretty much everything. You would be looking for the voltage on the TP3850 pack to drop off dramatically very quickly, much more quickly than your other two packs.

One possibility here is that the added weight of the batteries and the requried power to keep your heli in the air is offsetting the additional duration you have.