Low power battery backup
1) You need a power manager IC like the ICL7673. Summing power using diodes such as a Schottky 1N5817 will cause a Vdrop of .40 to .50 volts. That is too much of a penalty when your main supply is only 3.3 volts. You must use mosfets that do NOT have a reverse protection diode built in. That is why you have current flow in the reverse direction on each mosfet.2) If the design called for PNP transistors, what was wrong in using them? 30mA can be handled by any PNP such as a 2N3906. Bjt transistors will block reverse currents up to the voltage limit of the transistor. The current being consumed is so low that even bjt transistors cause very little power loss or voltage drop.3) For PNP transistors you need a 1K to 3.3K resistor on the transistors base in series with the Pbar and Sbar outputs, else a high base current will flow to the IC. Vcc should not draw more current than expected regardless of the transistor type.4) I looked at the IC datasheet and it shows what could be a 10K resistor from the base to the emitter of each PNP transistor. This is to make sure the transistors turn OFF when the drive signal (Pbar or Sbar) is OFF. The same resistors should be used if P-channel mosfets are used (with no reverse diode) , except the 10K resistor can be increased to 100K.5) I suggest you re-think your reasons for the change you made, and which transistor type is the easiest to install with no weird behavior such as reverse current flow.