Being Canada geese, I'm sure they say "excuse me" or "sorry" just before ingestion.
As for the chicken wire suggestion, someone asked me that once and I dug up a bunch of pictures and videos of engines on the group sucking up water and carrying baggage containers in their intakes to demonstrate how useless the wire would be, and how hard it would be to hold it in place. Also get them to think of a chicken (preferably not frozen) hitting chicken wire at 150mph
As for shutting down an engine automatically, I remember working on a quote for a bit of military gear that had the 'battle override' button. The kit was supposed to protect itself from overheating and other dangers, but if you hit the battle override, it would run itself to destruction, presumably on the basis that if it shut down you were going to get blown to smithereens anyway, so running it to failure might give you the chance you need.