I reload a lot of HXP. The primers are crimped but that shouldn't break your spindle. I haven't found HXP to have undersized or misaligned flash holes either.
I would be suspicious of the alignment of the spindle. 30-06 being such a long case, it doesn't take much of an angle on it to miss the flash hole. Also, loosen up the collet that holds the spindle in place. It should be just tight enough to punch the primer. The idea being that, if it hits an obstruction, it will slide up out of the die rather than break.