Two methods that have worked for me and others come to mind, and have been discussed previously, but on pre-1970 models which is why it might not have shown up on your search results...assuming you searched for an answer of course.
1. Pick a port, any port, behind the shuttle valve. Use fittings to adapt a grease gun. Cap off the other port. Then use hydraulic pressure to move the valve out.
2. The less finesse, more he-man approach is to heat it up (propane fine, don't need anything more than that), grab it with a sufficient glove (this is pretty important if you don't want a distribution block 1:1 scaled tattoo in your palm), and bang it down hard on a hunk of wood (so as to not dent the brass block).
I have Kevlar gloves that are perfect for this, and never spent the time getting the fittings set up for a grease gun, so you can guess which way I use.