Efficient voltage auto-selection using MOSFETs - does it make sense to make an auto-select between battery power and external power?
I ran some simulations with mosfets configured in the diode configuration all resulted in worse results compared to a dedicated Schottky diode.

In your simulations, you are not using the MOSFETs properly. You are wiring them up such that the rest of the MOSFET is gone and only the crummy parasitic body diode remains. In this case, it would have a higher voltage drop than a Schottky diode. This isn't the goal.
The goal is to connect the PMOS in such a way that the source-drain actually conducts and flows through the low source-drain resistance. It's just that the current happens to flow in the opposite direction than usual through the source-drain. You don't actually want it to flow through the body diode. The body diode's conduction can be used to jump start the process but once everything starts the source-drain resistance will decrease and current will flow through that instead of the body diode.
Circuits like this are not drop-in replacements for regular diodes. You can't just put them anywhere you want in the circuit without thinking like you can with a real diode because the PMOS gate has to be connected to the correct potential (and sometimes additional circuitry is required for that).

You don't need opamps.
You can use this circuit which I will steal from another user's question (Is this MOSFET upside down?) on this website:

With no external power (VBUS) the resistor is able to pull the PMOS gate to ground which turns it on and the PMOS conducts through the source-drain resistance rather than the parasitic body diode resulting in a very low voltage drop.
When there is external power, the external power overpowers the pull-down resistor and stops the PMOS from turning on, so the source-drain remains high resistance. However the PMOS body diode still tries to conduct, however, the Schottky diode has a lower voltage drop than the PMOS body diode so as long as the external supply voltage, VBUS, is at least as high as the battery voltage (and can even be a bit lower than that), the Schottky diode will conduct and cause the voltage at the PMOS source (the body diode cathode) to be higher than the PMOS drain (the body diode anode), thereby reverse biasing the PMOS body diode so it can't conduct.