Remington 35 Whelen ammo is notorious for causing the same, so I wouldn't recommend trying it.
I had to dispose of over 200 Remington 9½ primers due to a similar problem a bunch of em wouldn't fire, so I got rid of all of the rest of that lot.
If it's not defective primers, seating hard into the lands from what I've researched works sometimes, but forming a false shoulder on the case and then neck sizing it to desired headspace should solve the problem. For the Whelen, I'd run the brass onto a .375" expander, then neck size, IE: partial full length size, accordingly, see if that eliminates the problem.
The pic below is of .375H&H brass, used a .405" expander on it.
Tim
Right to left, Factory brass, expanded neck, partial neck sized, final neck sized.