I worked in a cuckoo shop for over 10 years and had this issue often, even had to change posts on new movements when a long post was required and we did not have any. At first I peened them in, however the thin plates and tendency to bend and trying to get it in at 90 degrees on some was frustrating. What I did was use one of those thin cutting wheels and cut a slot in the post about 6mm past the shoulder ground a bit of steel round stock to a wedge and tap it in, a bit of solder to hold it and cut off the excess with the same small cutting disk. Dose not take as long as it sounds, however it make for a nice clean job especially on a new movement.
If I understand correctly, he cut a slot in the base of the post and used a steel rod to force the slot open, securing the post in place. Then solder to hold the steel/brass together, or possibly hold the post in place too.