^Yeah, I didn't see that until later. You had it figured out. I was initially confused by OP's "schematic" and voltage readings. I was sure he had it hooked up incorrectly.
Anyhoo, this current limit of circa 3A is why this beautiful piece of kit for the $ is not very versatile. I think you need li ion or lipo battery smaller than matchbook before this is applicable. I want the low voltage cutout more than the max current, unless that max current is adjustable. If you want super small current limit to protect the circuit or battery, you can select the fuse with the exact rating you want.
What I would be inclined to do is to cut the voltage sense trace off the SOT part which measures the shunt current and ground that pin. This way, you retain the low voltage cutout, of course. It should be that simple. And it might be. But of course all sorts of funny things can happen due to the software/hardware algorithm in there doing all the weird stuff.
Addendum: You could maybe even use that pin as a RESET or on/off pin, for interface with any micro or whatnot. 150mV is above the threshhold for CMOS digital output low, anyway. Not sure about TTL or other stuff. But there is probably some criteria that must be met before it will turn back on, otherwise a short on the output side would make the output oscillate until the battery was drained below the line sense cutoff.... This would be weird, and it is why I still find it odd that OP measured 1.1V on the other side of the FET. The max current cutout on the circuits I have thus far encountered have to be reset with something like 4+ volts detected across the battery terminals (by plugging in the battery charger, temporarily, for instance). This could be the case for a simple hardware circuit, but this chip wears fancier pants than that. To get 1.1V out of a 40A battery, there's some high frequency oscillation going on. OTOH, his battery is so huge, maybe it resets the circuit just by being there?