Has anybody ever wondered why the gear doors get sucked open in the first
  place? There should be high pressure under the wing, now low. Maybe there's
  VERY high pressure inside the wheel well. If so, how does it get there?

Adam,

 

For main gear doors it may not be a matter of sucking them open because they may never get closed.  Those doors also have a cambered shape that may have them operating like a wing with their own lift downward once there is air flow and just before they would actually close.  The only Lancair inboard main gear doors with this problem appear to be on the Legacy.  Partially the cause is that they are so big.

 

The nose gear door is a different story on the LNC2 series.  The aft part of the door is beyond the hinge and usually is not stiff enough.  There is no real air pressure against the door from the outside because it is behind the cowl that extends several inches below the fuselage in the area in front of the door.  Finally, if the nose gear leg seal is not perfect (between the firewall and the wheel well), lower cowl engine cooling air can enter the wheel well and force its way out at the tail of the nose gear door.