Using the advanced hole feature, I select a far side countersink, specify a depth for the countersink, and make a matching through hole above it in the stack as "up to next element."  I always wind up with the through hole stopping short, so there's a revolved triangle shape of material rather than the through hole going until it all breaks through.  If I try to make the through hole Blind, I can't extend it without it throwing an error, and making it shorter only makes things worse.  Reducing the depth of the countersink gives me the opposite problem, where there is a flat circle at the bottom of the countersink instead of going down until cone meets cylinder.