I am from Canada and recently brought my TX to Portugal with me for the worlds, it was my first time travelling Internationally with a firearm.
A few things that come to mind;
No ammunition in the gun case (duh...) and no ammunition in carry-on
External case locks (mine were not TSA approved, I asked about this and was told I didn't require them, YMMV)
Trigger lock on the gun (I also put zip ties around the barrel/cocking lever to render it unusable, again)
Also good to have the serial number of the rifle in hand or memorized
I think as long as it looks secure and you have followed the airline specific guidelines you should have no issues. Honestly, I was a little worried having never done it before, but the whole process was very simple and easy...
There is no replacement for shot placement...