While you're at it, warm up the valve stem a little with a propane torch. Heat, spray some Kroil, tap with a hammer while it's hot. Don't get ridiculous about it, but getting the stem hot to the touch will help the mouse milk penetrate down the stem. Since you've got to pull the rocker arm assembly anyway to replace the broken one, putting a little heat on the valve will be a lot simpler with nothing in the way to deflect the torch flame. I've freed up a lot of stuff with the "hot wrench" over the years!
Jerry