A couple of Hints:
Home Depot
get a set of steel drift (punch) pins to carefully tap out the pins, honestly it is WAY safer
Dasco Pro Small Pin Punch Set (3-Piece)-34 at The Home Depot
I pretty much use the 1/16 almost 99% of the time but the price difference for the 3 pin set vs just one punch was minimal
For really stubborn rusted pins I use Kroil to loosen it all up
Harbor Freight I buy several of these every time they go on sale for $1.99 they last me about 6-8 months each, I polish the bottoms up a bit better before use
Search results for: 'flush cutters'
There are of course many others like these available but honestly I have tried using the "Better" read more expensive ones, but they last no longer and work no better
Using these two tools and patience I can pop safely over 90% of all the pins that come across the bench, for the other 10% I do much like you have outlined here but with small a Hand File