Seating the bullet deeper will increase chamber pressure and compound your problem.
Some more primer tidbits: SAAMI has standardized the flash hole diameter in rifle cases to .080" (about 5/64"). If you do the math, a 50,000 psi chamber pressure load will exert about 1000 psi through the flash hole and into the primer. A token increase in flash hole size of a few thousandths, will increase the pressure on the primer by 300-400 lbs (caused by the decapper pin). This would make a very safe load appear to be over pressure if you use the flat primer as an indicator. The pressure inside the case didn't change, just the pressure exerted on the primer changed. Some primers have softer cups than others. Using exactly the same load, one primer might flatten while another brand looks normal. I wouldn't put much faith in "reading" the primer.
Donna hit on headspace so I'll expound. The weakest place on a bottle neck rifle case is the point where the case wall meets the solid head. This is the place where case head separation occurs. Assume a rifle has an "in spec" headspace. When fired, the case will be pushed forward by the firing pin. Then the internal pressure will push the primer out slightly. As pressure increases, the case is driven back against the bolt face and forces the primer back into the hole. If the load is over pressure, the case will show a bright ring at the head/wall point. In extreme pressure cases, the head may separate from the body, even if the headspace is in spec. If the headspace is excessive, it's almost sure to cause a bright ring or even head separation with normal pressure loads. The movement of the case within the chamber will cause a primer to flatten too.
A cheap trick for testing headspace is to fire a case loaded with only a primer, (no powder or bullet). When the case is extracted, check the primer to see if it has backed out. If the primer backs out more than .005" higher than the head, it's an indication of excessive headspace.