One or two idle thoughts...
Composite fatigue. This is poorly understood, even by people who look for it for a living - this isn't to criticise them, just that the Human Race as a whole hasn't really come to grips with it yet. Similarly the basic strength of composite parts, when new, varies far more than metal ones.
For that reason, we apply huge safety factors to composite structure when it's approved. This should mean that when it's brand new you'd have to overspeed by (rough back of envelope sum) 50% to damage a composite component in the airflow, and if Piper got their sums right (which is by no means certain for the reasons stated above and not because I've anything against Piper) by at-least 18% to damage the door at any point in the predicted life of the aircraft.
Problem with the microcracking in composite structure that constitutes fatigue is that the only way really to spot it is to cut the structure open in a lab - which is rather pointless since you then can't fly it again anyway. The way it actually affects the structure is to make the whole thing weaker - a very different effect to metal fatigue which introduces small numbers of (reasonably) detectable cracks that simply create identifiable - particularly after a failure.
If you are really in trouble, rather than just being grumbled about call AAIB on 01225-510300, they'll almost certainly have some suitably qualified materials experts on their books that they can point you at. But, be warned that anybody good enough to do consultancy for AAIB is not going to be cheap.
On the other hand, one hopes that this was (okay it's borderline on whether it's a reportable accident or not but good practice says you report it anyway) reported to AAIB and they may look into this in ther own light and budget. It may be that they'll find something akin to what HiST suggests, and might want to make recommendations to Piper that would make everybody's life easier!
G