Could be the shorts shifting around and chafing (which could be that they're too small, too large, or just the wrong shape); could be the saddle is too wedge-shaped (see, I don't say "pear" any more
) and pushing you forward of the cut-out. I'm inclined to think it's more the shorts, if you're not noticing a problem until you're off the bike. This might be the time to try a dab of lubricant, only on the area that's bothering you, if you're not using any yet.
If it's saddle tilt, it's more likely that the nose is too high rather than too low, especially if you're not noticing extra weight on your hands.
Speed comes from what you put behind you. - Judi Ketteler