Nhyrum,
Assuming you haven't run into Berdan cases, I think your issue is probably the military cases, as described above. A lot of them, as well as Fiocchi cases, have drilled flash holes, and for some reason they do not use a moving drill guide with a nipple that moves up into the primer pocket (what I would do), so the drill tips extend into the pocket and tend to walk, resulting in off-center flash holes. I've long noticed this in Lake City brass with an occasional one pretty far off. In the Fiocchi's I've seen a few that were almost adjacent to the side of the primer pocket, and your decapping pin would wind up running into those same as the solid center of a Berdan primed case.
You can look into the cases with a bore light and the off-center holes are pretty apparent, so a pre-decapping inspection should let you segregate the ones with significant offset. If you use a deburring tool on the inside of your flash holes, most of the time those put enough of a chamfer on the hole that they will guide a decapping pin into place when the offset isn't too great. One way to decap offset flash holes is with a inexpensive
Lee Loader decapping rod and a hammer. These probably give you the most lateral wiggle room to find the flash hole, though I have to say I have a Lee Universal Decapper semi-permanently mounted in an old Challenger press on a portable plastic stand that has only once had trouble stopping against an off-center hole. If you want to use the Lee Loader rod and don't have a Lee Loader's shell base, just use a of 2×4 or, better a piece of hardwood block as a base. Dill a shallow hole wide enough to capture the base of a case, drill a deeper quarter inch hole in the middle for pin clearance and spent primers. Put a metal washer in the bottom of the hole to better support the case as you hammer the spent primers out.
Once you've decapped all these, cut or swaged the crimp away and deburred them, your standard dies should work OK from then on, though I would dispose of any where the flash hole is grossly off-center. Up to about half a flash hole diameter off-center should be OK.
In addition to the above, I'll add that I've broken a few decapping pins in RCBS, Redding and Lyman dies over the years. Almost always it turns out the pin chuck has loosened. Use the removable blue Loctite 242 on the pin chuck threads and they will last a lot longer.