Don't forget, the battery isn't "pushing" current. The atomizer is "pulling" it. The only way a "high drain" (translation: high maximum discharge rate) will make a difference is if your regular battery isn't capable of supplying the current draw. They should very much be able to supply the rated max discharge rate and usually much above that. So... the question is: what's the max discharge rate on the TF's? I'd expect it to be 2C or better? (hmmm, appears to be 1.5C). 2400mAh at 1.5C would be about 3.6 Amps? and I'd expect them to do better than that in a pulsed application maybe? I guess that would depend on the trip point for the pcb?
Using the IMR numbers
3.9v @ 2.2 ohms == ~1.8 Amps
shouldn't be a problem and you wouldn't expect to see a difference?
3.9v @ 1.8 ohms == ~2.2 Amps
Still shouldn't be a problem.
What I don't understand is why you're seeing a voltage drop with the stainless spring? Was it just the battey voltage tapering off because of the previous test's usage? More resistance with the stainless spring, the current draw should have been even less, so potential for voltage drop less as well...
I mean, I am under the impression that there is some small voltage drop between resting and loaded (due to internal resistance of the battery?) but outside of that I thought you should only see voltage drop if the battery wasn't able to meet the current demand. Then you would see a voltage drop to balance Ohm's law equation.