Turn the gun upwards and soak the base pin with a penetrating oil letting it run the full length. Be patient, it went it so it will come out. Thoroughly clean all the contact points, and the base pin itself, once it's out and run the base pin in completely without the cylinder until it removes easily. Clean the base pin hole in the cylinder, too.
I went thru this exact scenario early this week with a Colt. What seemed like a PITA really was quite simple.