Great question and great answers!
I used to fly for hunting trips and had the extra decision factor of limited funds (after buying the tickets!). My case was a simple clamshell injection molded double case. The difference was to reinforce the six sides with fitted panels of masonite. Each side, end and flat was protected with a 1/4" tempered masonite strip or sheet that nested between the plastic and the foam. The idea was always to keep the case from flexing and racking in handling, without going overweight or oversize. The particular case had six or eight flights with no rifle damage, only a busted hinge. I invested in rolls of duct tape and tie-wraps so as not to depend on the flimsy closures. I've never had to go cross border.
The advice about separating the receiver and barrel from the stock makes really good sense. The more length you have, the more handling "challenges" you are giving to the luggage gorillas. Shorter means the case will not get bridged between other cargo, and less likely to be dropped because someone gets overbalanced. You have to fire sighters anyways, so that is your chance to settle the action before the match.
One final thought. There was a CANFORGEN today that Westjet and Air Canada had just agreed to a free extra luggage deal to serving and retired military members. Just present your ID card or record of service card to get two, three or four extra pieces on board for free. Even if not every CGN'er is eligible, it pays to always ask about discounts, deals and benefits before accepting the first price offered.
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CANFORGEN 110/14 CMP 047/14 071213Z JUL 14
WESTJET AND AIR CANADA ENHANCED BAGGAGE ALLOWANCE
UNCLASSIFIED