The rules are not crystal clear, but technically you should NOT have TSA locks, though nobody will stop you. The process is supposed to be:
1) Check in, declare firearms. Sign the little form and open the case, put form in and LOCK it
2) From here on you can't touch it, they take it and will typically suggest you don't go through security incase TSA wants to look in the case. They suggested 20 minutes to my wife and I. We grabbed a coffee, sat and chatted, then went through security no issue (note, some smaller airports might have TSA right there, then you're good!)
The fun is picking it up at baggage, that process seems to vary. In SD it came out in "oversized" section - so find that, it's around somewhere. In Boston we were called to the luggage office and had to show ID to get it back.
One other suggestion if driving isn't an option: Check first class prices, has the following benefits:
1) Typically your first two bags are free!
2) Typically your first two bags can weigh 70 lbs, not 50 lbs (matters when you check in and fly with boxed meat after a successful hunt)
3) Bags are marked "priority" lowering the chances that anything misses a flight.
4) Factor in drinks and food on the plane are free.
My wife and I flew home from our hunt in first class. When calculating the fee differences we figure we each "upgraded" for $50 for a cross country flight, which we then probably drank and ate that much :-) You do NOT have to go first class both ways.
We will drive from now on. to get where you are going to hunt, it takes a full day anyway, since you won't have a direct flight. We went Boston to Denver to SD. Most hunting spots are either near small airports or long drives once you land. You can drive most places in 2 days (for us, from NH to our WY hunt would have been 30 hours driving - 2 long days)
Plus you save significant baggage fees (still cost us $300 to bring home 2 deer and 2 antelope, on top of the free 4 bags we had)