If for you is not a problem, can you please try also another thing ?
The voltage at the sides of the 6.2 ohm resistor, and from ground to the reference pin, in both the conditions, 3 and 3,7V batteries (or 6 and 7,2V, if you use a power supply) ..... for see if this can influence the loopback/reference part of the circuit ..... just trying to understand why it vary, and this can be one of the reasons.
Ofcourse, if for you is not a problem and don't cause you difficults ..... if you can do it, i marked the points on your image, for more easy operations (for the reference voltage, is more easy to measure it there, than from the IC pin).