Hello overdog,
The reason the 4xNIMH cell configuration works in driving a SST-90 is because of the very high discharge rate for the size of the cells... The fact that the ST-90 can handle that current is important. Consider, a normal AA NIMH cell will have around 2AH capacity, when delivering 7-10 amps, it's running in the 4-5+C discharge range, which, while hard on cells, is not unsafe per-say with NIMH cells because they are safe and tolerant of abuse. Lithium Cobalt cells should not be discharged at a rate higher than 2C (for most cells, some should not exceed 1.5C, and I personally always recommend trying to keep all LiCo cells running in the 1.5C or lower arena as 2C rates have been shown to dramatically reduce cycle life). With that in mind, a 1.1AH 14670 should not be discharged faster than around 2 amps. However, if we did take 4 unprotected 14670s, and try to drive say, 3 SST-90s, it would likely "work" in so far as the drive current would reach whatever the maximum current the cells could deliver is. Without a protection circuit, I'd estimate a similar scenario as with the 4 NIMH cells driving a single LED, the cells would deliver as much as they can produce through the effective resistance of the configuration, which would result in a discharge rate far above the safe rate, possibly upwards of the same 7-10 amp range, obviously, if the LEDs in question were P7s, they would be severely over-driven and likely fail quickly.
As you found, the protection in the cell doesn't even allow for these levels of discharge, so the above scenario is based on a hypothetical unprotected application.
Now.. Lets explore the concept of using 4 14670s to drive 3 P7s in a proper manner. This can be done if you use an appropriate driver and take into consideration the total power consumption from the cells and modify the output to be at or below the 2C limit for the cells.. Here's how this is done:
The total stored energy of a cell or battery of cells can be stated in watt-hours. A very rough way to estimate the watt-hour "rating" of a pack, is to multiply the capacity of the cell by the nominal operating voltage. For LiCo cells, 3.7V is about the average operating voltage under most common loads. De-rating capacity a bit in these estimates is always a good idea. So, a 4x14670 pack is roughly 4x3.7Vx1AH=14.8WH. Power flowing from the pack is stated in watts. A 1C discharge rate for the pack would be right about 14.8W, lets call it 15W. A 2C discharge rate would be about 30W. For a 3 cell pack, the stored energy would be ~11WH, and the maximum safe discharge rate would be around 22W.
You'll see where I'm going with this in a minute...
The power consumption of a device like an LED can be expressed in watts also. A P7 running at 2.8A with a Vf of around 3.6V would have an operating power of around 10W.
Now, if we use a true current regulator, lets just assume a 100% efficient scenario that can boost and buck without limitations (doesn't exist but for this state of the comparison lets assume this for the time being)...
3 P7 LEDs are going to draw 30W if driven at 2.8A, with the 3 cell pack, this is over the maximum safe discharge rate, however, if we bump it up to 4 cells, and have the regulator in place limiting current across the LEDs to 2.8A, the power consumption will still be 30W, but the extra cell in the pack will reduce the load on each cell just enough to be operating safely.
In this example, we haven't taken into account the efficiency loss of the regulator. A well built and relatively expensive buck regulator would operate above 95% efficiency in most cases. So, the power consumption would actually be ~31.5W assuming 95% driver efficiency... IMO, this is pushing those cells too hard, I would suggest trying to get down around 1.5C, or ~22.5W on the 4 cell pack, or around 21W through the LEDs after efficiency loss, which translates to a drive current of about 2 amps instead of 2.8A. Which, would still be very very bright, and would actually probably be preferable since the efficiency of the LEDs would rise with the lower drive level, which would further reduce the heat that would have to be dissipated.
Hope that helps some:
-Eric