I made a bushing two times as long as the button and the same OD as the barrel. Bore it so the button just slides easily. Clamped barrel and bushing in a long "V" block so it was right on center under the hydraulic cylinder. There was a small divot in the center of the cylinder top locate the top of the push rod. I used six inch long HSS rods just smaller than the bore. ground a small taper on the ends so they would not catch and score the rifling.
Push to bushing, retract, remove bushing, push to barrel, retract, repeat.