not possible - especially not with an xml2 … xpg2 has a lower forward voltage, but once the battery is partially depleted below the forward voltage output will dim
In order to maintain a constant current or output (regulated), the power supply have to be constant. (Running of a rectifier or DC supply).
No batteries could do that.
You are talking about a linear driver. A buck/boost driver will maintain contant output to the LED from a voltage above Vf to a voltage below Vf.
the only p60s i know of that do that are malkoffs… which are setup for more than one cell (usually)
Yes they could - if a boost circuit is used. As I said earlier there are several of the more expensive lights that do this with one Li-Ion cell. Zebralight, 4Seven and a lot of others, just no P60 modules.
A boost driver draws more current from the cell as the voltage drops, that increased draw is converted into the voltage required for the LED to pass the intended current. Look up one of HKJ's boost driver reviews to see it in action.
A good reason to learn how to solder and build your own dropins. 
Is this the highly touted Shiningbeam driver? http://www.shiningbeam.com/servlet/the-133/3-dsh-Mode-Regulated-Circuit-Board/Detail
...because, well, that's just a Nanjg 101-AK, maybe with custom firmware. Firmware can't affect the regulation at all, though they may be using a lower than standard low voltage cutoff. Still doesn't affect what happens when Vin and Vf butt heads and output current starts to fall.
No… read post #11 again carefully.
NO YOU read #14 again carefully, that's the one I didn't pay enough attention to. That's where the 1.4A driver is mentioned that I went looking for. SORRY TO HAVE WASTED YOUR TIME! 
Here should be a graph:
Bipolar much. Hahaha.