The problem is the used brass you bought. Thats not to say there's something wrong exactly with them; they probably go back into his chamber perfectly.
Treat every instance of used brass from different as a salvage operation. You can go decades without a problem, but sooner or later you'll get what you got.
Chambers vary in size, and dies vary in size. Not every case fired in every chamber can be resized with every die to fit in every other gun. If they made the dies small enough and short enough to guarantee it we'd all be screaming blue murder about short case life.
First thing to check is that your FL die is set to cam over hard. I don't care if your die setting has worked just fine every other time, because this isnt every other time. Perhaps you've already done this, it is the logical first step.
If that doesnt work, a low buck trick is to slip a few thou feeler guage between the case head and the shell-holder. Remember to take the decapping pin out first. Size a case like that and see if it chambers. If that works, its probably the only time you'll need to do it. Cases fired in a rifle tend to go back into the same rifle.
If that doesnt work, a small base die usually will. We used to call the .300 version a BAR die. Not so much because the Brownin gas gun needed more squeeze; it was more that those owners usually shot factory ammo and were a source of free or cheap brass. Their chambers tended to be huge, and SB die would get the cases into our guns. Usually once was enough; then you're back to the theme of cases fired in a rifle tend to go back into the same rifle. The .300 Win SB die is a handy thing to have around because with the guts taken out of it it can put a little extra squeeze on every Mag that is shorter and a smaller caliber. That's most of them. Thing is, new dies cost money and you have to have enough salvage brass to make it worth while.
The Willis tool is a handy tool, if the interference is right tight in front of the belt its about the only thing that will work. (A black Sharpie is handy for telling where the problem is) Its not that common until you do what doing. I got mine when I had a few hundred once fired Weatherby brass fired in a rifle I sold and wanted to use in one I'd kept. Paid for itself on the one job; but it cost money and you shoukd have enough brass to justify it. If you do end up with one; it works on all the H&H based cases.