I have carried significant amounts of PM's both in the USA and overseas - as long as you tell a reasonable TSA agent that you need a private screening in advance they will accommodate you. Only clumsy experience was a couple of years ago in Amsterdam when I specifically told the security person that I had bars of precious metals and they proceeded to take them out and inspect them - all were then put back into my bag and I went on my way for my connecting flight.
Hey, it would be easier than that to take over a plane with coins by taking quite 5 oz pucks with you. If you throw them like frisbees you would have a lethal weapon. They wouldn't stand a chance.
Wrong, wrong, wrong! Also completely wrong. I suspect that you haven't been on an airplane since 9/11/01.
Totally untrue. TSA inspects bags at their discretion and there is no requirement to find the passenger to observe it. They have paper notices they put in the bags that are inspected. Never never never put anything of value in checked luggage.
That has been my experience as well. I had a bag from MN to GA have its lock broken and a paper notice placed inside. No one tried to find me to ask I open it. Maybe they do this as a courtesy in smaller airports, but I have never heard of it done in larger ones, at least since 9/11. Regarding carryons, excellent advise here for you OP. Like Treehugger said, do not surprise the TSA and ask them for a private screening. Rest assured coin dealers fly with millions of inventory monthly around this country to and from shows, and from my understanding this is what they do.
Just do a roller carry on. Try not to let your airline see it is a heavy bag as some have weight limits to their carry ons. The key is just act normal. Don't panic because someone bumps you, nobody knows what is in your bag. Like others said private screening if needed but I rarely get screened for coins. Here is my one tip. Pack the coins so there are vertical when they go through the X-ray. I was told this by TSA. If they can see through the bag good chance you will just walk through. Since I started this packing I have not been stopped once for screening. I normally have gold and silver in my bag and sometimes lots of it. You will be fine.
I just read some of the other posts, do NOT check this bag. You can lock a carry on but will have to open it if called for screening. I travel every few weeks with coins, it is not hard just use common sense and don't over think it.
My advice would be, if you have a firearm, put it in the bag, declare you have a firearm in the bag with all your other PM's. You'll have to check it in but I assure you, they will not lose your bag or anything in it. I know a guy who takes his firearm on every flight he takes (well, if he has to check luggage in) just so his baggage is never lost.