5V power supply with battery backup controlled by a single enable pin

Question

Requirement:

1. at least 1A output

2. integrated Li-Ion battery charger and boost

3. a single pin to switch on/off the circuit in all three conditions:

   i) external powered without battery

   ii) external powered with battery

   iii) battery powered

4. UVLO

5. The circuit must be on when EN pin is float

6. The EN pin must tolerate 5V input

Theory of operation:

1. A USB load switch to handle condition i and ii, VIN is 5V.
2. A battery charger and boost regulator connected in series to handle condition ii and iii.
3. UVLO implemented as a voltage supervisor to disable boost.
4. (This question) a logic input to enable/disable USB load switch and boost at the same time.

Design 1:

A N-FET give EN pin the power to disconnect voltage supervisor from ground, forcing boost regulator to shutdown when EN is low

Design 2:

A battery powered logic gate to control the boost regulator.

In both Design:

-R5 pull EN pin high to VBAT

-D4 make sure EN does not pull VBAT to 5V

-C2 is a dummy battery, which should in theory make condition i and ii identical.

Are those designs reasonable, is there a simpler way to achieve this?