I want something for my power that acts like a diode, but without the voltage drop, to protect the circuit from damage if the batteries are connected the wrong way. Is this even possible?
A MOSFET can be used to protect a circuit with a low voltage drop. See the following for more information:
I am planning to use the LTC4365, but that's overkill, because it has overvoltage and undervoltage protection built in (which I have a use for because it may be used in an automotive environment, but you might not.)