Rectifying reversible polarity battery with minimal power loss
As mentioned above, mosfets have leakage currents that might be in the same range as your minimum current requirements. The blocking mosfets have a Drain-to-Source Leakage Current and the conducting mosfets will have a Gate-to-Source Leakage Current.  

If these issues can be tackled, then your suggested circuit will work nicely. Therefore:
search internet for (ultra) low leakage mosfets.  

I found that way the nice CSD23381F4 12V P-Channel FemtoFET TM MOSFET.

It has:


really less than 100 nA IDSS (because VDS is max -4.2 V instead of -9.6 V)
really less than 50 nA IGSS (because VGS is max -4.2 V instead of -8 V)
less than 300 m&Omega; ON resistance (because VGS &lt; -2.5V and IDS is max -0.020 A)
Support single cell Li-ion (3.7 - 4.2V) because of its low VGS and a VDS of -12 V.
costs only 0.05 / 1ku




DISCLAIMER
I don't know if you want to make a PCB or even a breadboard (please don't do the latter), and were planning hand soldering: then this package might be a problem.
This answer is more to point out what keywords to search on and what parameters to consider. It's also the reason only a PMOS is suggested.