I don't believe it's the surge in momentum (acceleration) you feel, I think it's the surge in acceleration. (integral of acceleration, I think?)
The acceleration undergoes a sharp jump and then levels off, (which is in line with what you feel) while the momentum starts increasing more quickly, and continues in that way.
Hope I made sense. It's something I've thought about a bit, though don't have any fancy textbooks handy to back me up... but the human body appears to feel the change in acceleration, much more strongly than 'just' the acceleration, which can mean the game doesn't feel right, because you're not getting 'tricked' by the g forces.