Not a whole lot to know about a countersink (I have been using one for my military brass primer pockets and cleaning up case mouths for nearly 25 years). The primer crimps displace a small amount of case material at the top of the primer pocket. A countersink (I've been using a 60 degree high speed steel) cuts the displaced metal and "opens up" the primer pocket allowing for a clean/easy insertion of a new primer. Sometimes I chuck one in my hand drill or power screwdriver and it takes only a second to cut the offending crimp out...
Where did you get a 60 degree counter sink ? All I have found in Lowe's and Home Depot and Ace hardware is 82 degree counter sinks.
Today at a gun show I picked up a used RCBS pocket swager combo 2 for $10.00 The guy said the rod in it is one he bought on ebay and is extremely hard and won't bend.