Adapting a low voltage cutoff circuit

I'm making a project that will run an ATmega328 5V 16M on a 3.7V lithium battery boosted to 5V.

I'm planning to use this charging board:

It has a low voltage cutoff at 2.5V, but it turns back on when the battery recovers to 2.9V! I'd like to make it stay off until the 5V USB is connected, so it doesn't damage the battery by cycling it down. I figured out how to do it using 2 relays, but that would be fairly large and draw ~150 ma.

I'm new to circuits and arduinos so any help would be great!

Move the battery sense to the input 5V USB and rescale the sensor divider values.
Most good Li-Po batteries have, Or should have a battery protector board installed…
I’d use the attached data sheet on the TP4056 and make your choices…

Doc

TP4056.pdf (59.5 KB)

Hey, thanks for the reply Doc! I don't think my post was very clear though, what I want is for the board to stay off until USB is connected only AFTER the low voltage has been triggered.

I think it could be done with a NOT gate on the USB going into a NAND SR Latch R, with the charger board's output to the S. The latch would controls a Mosfet for main power cut off.

I would then have the USB control a relay to kill main power to avoid using the invalid 0/0 input when plugged in with a dead battery.

Does this sound right? I'll draw a diagram when I'm home later. What type of transistors should be used for the logic gates? They would need to be controlled by 2.5-5V.

How much power would an NR Latch draw? In the case the battery was dead and no charger was connected.

Okay here's what I came up with:

Does this seem right? Do I need some resistors in there? I read somewhere that the mosfets can use a lot of current without a resistor.