A shooting bag and vest? Are you travelling with a gun? If I were, I'd put em with the checked baggage. Obviously nothing wrong with carrying them but I just don't need any hassle to add to my already pissy attitude when flying.
I always have had my shooting vest that I use for doubles and my leather box carrier along with hull bag and towel on a leather belt in my carry on. This is in case they miss place my checked bag. This has happen a few times and I was able to still feel comfortable with my stuff, rather than having to borrow or buy new stuff. Just make double sure that all loaded shells are removed.
I also have my ear plugs in my carry on.
So far very little problems with TSA, sometimes they will hand check the bag and most often the x-ray is enough.
I flew at least twice from SAT to PIH with roughly 1000 empty Remington hulls in my checked luggage, packed several hundred per bag in Remington plastic wad bags, so I wouldn't worry at all about nitrate residue. Also I never had a problem checking my shotguns at PIH, SAT, or GEG. One flight, booked with frequent flier miles, went PIH - SLC - ATL - SAT on the outbound with tight connections, and SAT - DFW - SLC - PIH on the inbound, and my guns arrived with me. I wouldn't worry about it.
I was under the impression that you are a high-milage frequent flier who's done a lot of international travel with your guns.