WOW! that has seen some hammering. Normally those will slide through the escutcheon plates. I am wondering if you took a thin blade ora ice pick of sort, ifyou could not drive then out. And when you get them out, REPLACE them.

Since they did fit through one side of the escutcheon plate they "should" fit through the other, but I hate to tell to drive them through in case something is damaged.

So I will leave it to you. Normally they do side through and out. Its up to you if you want to try to drive them through. And yes that is one of the old Mountain Rifles.. you have a great rifle there.