Thanks Wawa. When I wrote "I would remove the RC filter" it was because the RC filter didn't feel right. But with a ratiometric sensor, the RC filter works against the ratiometric match between the sensor and the Arduino. Thanks.
KevinRoach, don't try a electronic solution. The sensor should be connected directly to the Arduino for best results. Also connect all three wires of the pressure sensor directly to the Arduino board. Do not, for example, connect the ground wire to other ground wires.
You can do a lot in software, but I have already mentioned that a few times.
The damper chamber that I mentioned will really help a lot. For example a plastic jar of 0.5 liter with a screw cap. Fill it with polyester fibers that can be found in stuffed animals. Make sure the inlet and outlet are sturdy and don't leak.