I have since vaguely changed my tactics. I fly quite frequently with my bike - around 25 flights last year probably, to the US, Australia and Italy from the UK. After the incident where the (carboard) box was opened and left that way (it was a long bike box, and they cut it open down the side, not along the top), I got a fresh bike box, and cut it down in size to be as small as possbile. I reinforced all the holes to carry it by, and I applied a vast amount of bright red tape along all the edges I didn't want them to open it by, and didn't actually tape the top closed. Instead, I used three luggage straps to secure it. Results so far - 2 flights, opened by security both times, no problems.

For further info, every single flight I've been on to / from the US has involved it being FSA checked, so it is very likely to be opened.