Reverse polarity protection for a very low voltage devce
Did you see (and understand) Spehro Pefhany's comment?
I take the liberty of turning it into an answer because that's also what I'd suggest.

Add a diode in front of your circuit that shorts the voltage if the battery is reversed (=V2). In that case the (resettable) fuse will break the current flow. If the battery is not reversed (=V1) there is almost no voltage drop (only a small one across the fuse because it won't have 0 resistance):







simulate this circuit &ndash; Schematic created using CircuitLab

The diode must pass enough current at reversed polarity to deactivate the fuse.
The fuse, of course, must be able to sustain enough current for supplying the circuit in normal operation but must blow/deactivate if the battery is shorted via the diode.