Looks like your seating die is too far in and bulging the cases. Dies vary a little in the way you set them up. Some directions tell you to screw the die in until you make contact with the primed and charged cartridge then back it up a turn. Some tell you to run it into the ram and back it out. Then you'll need to seat the bullet without a crimp to get the over all length. Then you back up the seater so it won't push the cartridge into the case further and you adjust the die in until you get the grimp you want. Then run the seater back down until it makes contact with the properly seated bullet. Judging by your bullet, your trying to seat and crimp at the same time. Reset your die according to the directions for your set of dies and a roll crimp and try it again. That should fix it.
Back off on the crimp until the shoulder collapse goes away.
Make sure your brass case mouths have proper chamfer and are deburred, the groves on the TSXs could be catching. I would also recommend, using a Lee crimper and crimp them after they are seated.
I use the Lee crimpers both both 375 H&H and 45-70 and I'm very happy with the way they work, does add one more step but worth it for me.
"I refuse to let the things I can't do stop me from doing the things I can"
Assuming that you've FL-sized before trimming, I agree with others that your seating die is down way too low. Back the stem out a whole bunch, unscrew the die and start over. Run the case all the way up, screw the die down until it contacts the case, then back the die out one full turn, tighten the die and adjust your seating depth with the stem. One other comment...I stopped crimping for bolt actions a long time ago. I learned from our moderator Professor Murphy that you really don't need to do it, and he is absolutely right. I have handloaded for that wonderful 375H&H for over a decade. I really like 270 TSX's in mine.
I concur with Doc. I've been loading the 270TSX and the 260gr. Partition for only 2 years but haven't seen the need to crimp.
In fact I don't crimp any of my centerfire ammo from the .204 to the 375 H&H. I try to ensure straight necks so as to maximize accuracy. The last thing I want to do is purposely crimp (bend) it. But, to each his own.
But the others have it pegged for you. Your crimp is way too aggressive.
Foolishness is a moral category, not an intellectual one.
You are correct Doc.....Seating die body screwed down too low. Crimping on the seating stroke will wrinkle a case. If a crimp is desired, readjusting the die with stem up and body down to desired crimp, after the seating operation. And that's true, I don't crimp until we get to big bore and then only if there is a crimp groove and with perfectly trimmed cases. I am crimping my 500 N.E. and that brings better accuracy with the double but the 375 H&H doesn't need it. It's easy to push the neck down into the shoulder causing the bulge at the shoulder.
Is there nothing so sacred on this earth that you aren't willing to kill or die for?
I appreciate all the help! I'll let you guys know how I make out?
My rule of thumb is, no cannelure - no crimp.