You might want to have your static system checked. It is likely the static plumbling is dis-connected/leaking between the instruments and the static port which is at the bottom of the fuselage centre (roughly below the aft cabin seats). This static tubing is a thermo-retensive plastic, you heat it up to push it on-to the alloy fittings. The 'B' nuts on one of the adaptors could also be loose.
Strange really, I have never come across a squirel where the cabin doors seal well enough to create a cabin pressure differential so easily.
Haven't touched a '350 for a while but I remember some S/n's have two static sources at the location I described (pretty much next to one-another) and some only have one.
Otherwise, stop sticking your bl..dy hand out the window!!
