I am *VERY* familiar with the falstad simulator. I use it all the time as most who know me are aware.
It does not do MOSFET's correctly at all, it's an open bug that has been reported to Paul..... Use the model for "Analog Switche (SPST)" under "Active Devices" right click menu. Use a backward Schottky in parallel to simulate reverse conduction. You can make them effectively P-channel by right clicking them, clicking edit, then checking the box that says "normally closed". You can also change the on and off resistance in the same menu.
+1 if you feel this was helpful. Thanks.
Edit: Paul chose to use a symbol for the MOSFET's that shows what direction they conduct current when on. This is of course wrong.