It appears breaking and bending pins is an occupational hazard for anyone who reloads and I'm not immune...what I do use a universal decapping die on all my cases rather than the FLS incorporating decapping pin etc of the caliber reloading....I do tumble them first but after decapped tumble them again - I then use the FLS or neck die on them and usually with the pin removed (truth be known I never bothered replacing them when they broke )
Why I went this way because after bending a few rods or snapping pins on some brass I looked at why and found many did not have perfectly centered flash holes and some decapping rods did not have the flexibility to move slightly to find the holes and align especially for the smaller calibers such as the 22AH, 222R etc.....that caused most of the problems hence the universal decapping die...
I have also drill bits like previously posted but found the cobalt ones best - just cut to correct length needed and round them down with the dremel ....they tend not to deflect or bend as some pins do but conversely if you put too much pressure on it, the rod itself will bend rather than the pin - some manufacturers design them for that purpose.
Firstly though I would check your flash holes and those way off discard as you'll always have problems with them...just not worth it and then take measure if you still get problems........hope that helps......Lee