I'm thinking that you are using an incorrect nomenclature, I don't believe that you can put a gas check on a jacketed bullet; and....the Barnes TTSX bullets are jacketed bullets. First question does the bulging happen with any other bullets or just the Barnes bullets. From the photos it looks like what Laelkhunter wrote in his reply could be happening. You could have you seating die set a little too low where it is crimping the mouth of your cases. I don't use the TTSX bullets in my .270, however I do shoot a lot of Barnes bullets in my 35 Whelen and 358 Winchester. If the case mouth is not chamfered properly you will get scraping of the bullets, like in the far right cartridge in the photo. I also use a nylon brush with graphite on it to lube the case mouths before sizing. I've found the jackets on the Barnes bullets to be softer than regular jacketed bullets. I also use a piece of "4 O" steel wool after I chamfer that case necks to smooth up the sharp edges made by the chamfering too. lOr you could have an undersized expander ball in your resizing die.. Recently I purchased a Sinclair expander mandrel tool for my .270AI, it made a great difference in resizing the case necks; after the .270 expanding mandrel I bought one for my .35 calibers. The first time that I used it, I could not believe the difference between it and the expander ball that comes with the regular die set. All of the responses you've received here are all good suggestions. Did you try measuring your brass to see if the brass fell within the proper dimensions before seating the bullets. Try checking the depth of your seating die to make sure that it is not just kissing the top of your cases while seating your bullets; your .270 brass could have stretched a bit. Run the ram up to the top, then run your seating die down until it just hits the top of the casing, then back it off a half-turn and see what happens to your reloads.