Long ago and far away, on the way home from the 2009 F-class World Championships, a few bright sparks did something similar.
The ammo had all been shipped ahead to jolly old England by a team sponsor before the event, went through customs, held in secure storage, etc. etc. All we had to do was arrive, pick it up, go shoot (and win, yay us!). But some folks didn't plan ahead for the extra 15 lbs of spent brass. One or two had the bright idea that since it was *spent* brass, not live ammo, that it would be okay to put it in their carry-on. And... queue the shit storm. Obviously, the airport security were not on board with that idea. Questions were asked, resulting in them literally holding the flight as the airline unloaded their luggage so the cops could go through it, having a raging shit fit about all the spent ammo (and some remaining live rounds) loose in baggies or ammo boxes (not locked cases of their own). Meanwhile, our guys are saying "We just want to leave your damned country. Promise we'll never come back! Really!"
As an aside, *following* that little international incident was when Heathrow / British Airways began requiring 'proof' that any spent cases had been ultrasonically cleaned before they could be transported via checked luggage. No f'ing idea what brain trust decided that would do to make anything 'safer', but then again, it's England.
The group I was with was on hearing about all this via text and calls while we were taking a side-trip over to Ireland to shoot a little match there with some of our buds. We were all queued up in the line for the ferry from Hollyhead to Dublin with our hard-side long gun cases, binders of fire-arm permits, passports, everything, ready for the full-body cavity search by this point. Definitely getting the side-eye from everyone in line. When we finally got up to the counter, the customs agent started flipping through our binder(s) of permits, asked what our business in England had been. The team captain replied "well, we were there for the long range World Championship". "How'd you gents do?" they asked. "We took 1st place, and beat the Brits." said the captain. The custom agent looked up, smiled, closed the binder, and just wave us on through. End of inspection. They even wheeled our gun cases around *past* the metal detectors. We did about panic when we got to Dublin and we were trying to locate our gun cases - only to find them waiting for us stacked in a pile on the pier
But back to the point... that's two pretty solid votes for "checked luggage". And if they ask why you're bringing extra projectiles... well, it's up to you whether you want to try telling them that it's for reloading your ammo while you're there. If the bullets match your hunting guns in caliber, maybe. If not... they might get a bit prickly about attempting to import things bypassing customs. Just sayin'