Just to add to the confusion...err, I mean present other experience and viewpoint...
For a gunbox I usually just use a $10 plastic case that has an integral handle that allows me to put a standard combo lock around the handle, thus locking the case. It is small, light, cheap, can hold two guns, and meets all the specs. I usually put the ammo in my "sharps and fun stuff" bag -- a dop kit that I put in my knife, pepper spray, and any other pointy/"verboten in carry-on" objects. The dop kit lets me find all the pointy things quickly at the other end. No one has ever asked to see the ammo.
I personally would not take the slide off of a semi-auto, because it's at least one more step, maybe more, at both ends of the strip. I.e. you have to take out a take down lever or pin, or actuate the Glock whatsit, take slide off, put the takedown pin somewhere where you won't lose it, etc. I have flown my Browning HP and a Kel-Tec a number of times, and cranking the slide back half an inch is no biggie to show it is unloaded. (More than once I have simply pointed to the empty magwell and had the agent say "OK!" I chose not to educate them at that point, just smiled and locked my gun back up). When I go to the airport, I carry my loaded gun into the restroom in the non-secure area, unload it and stow it. (I wrap my magazines in foam and stick them into a "original manufacturer's packaging" ammo box that I have reinforced with clear tape). At the other end, I reverse the process.
For some reason I have gotten a lot of white "this firearm is unloaded" tags, rather than orange. As others have noted, sometimes the agent says put them on top of the locked gun box inside my suitcase, sometimes put inside the locked gun box. When I point out it doesn't make much sense to put it inside, they just shrug. Rules Is Rules and vary by airline. Really doesn't matter I think, because I think the real reason for the tag has nothing to do with security -- it is so if your gun IS found to be loaded, you can't say you didn't know it was against the rules and the authorities can make their charges against you stick.
Sometimes TSA looks through the bag, sometimes not. I of course have the only key to the gun box, but I use zip ties to secure the zipper. The TSA guys and gals have generally been very helpful about putting on the zip ties -- I just hand them one, ask them to put it on, and they do. The even helped me figure out an alternate method one time when the darn little zipper pull thing broke off at the inspection station. (Hint if you go the zip tie route -- keep a fingernail clipper or small scissors in an outside pocket of your luggage so you can snip off the zip ties on the other end! You can use a key to saw thru a zip tie, but it is hard work). Seems like one time they asked me to open the gun box. The took a peek and told me to close it. Dunno what that was about.
I have noticed sometimes that my bag will have a blue dot or a marking on the luggage transit tag, but I have seen those on many other bags -- it seemed to me to be more of a "this is a bag we looked at." One time that I can remember i had a note inside my bag stating it had been looked thru by TSA after it left my possession, but right now I am not even sure bag had a gun in it -- may have been on one of our overseas trips.
Traveling with the gun is not completely hassle free, but after a couple trips you figure out how to make it easy on yourself. I have not had any trouble. Of course, I only fly to CHL friendly states.

Not unusual for there to be three or four people declaring guns when I check in. Do allow extra time at the airport for it tho...
Happy traveling.