I have to agree with Rich e, about the danger you are in using 4 Fg in the barrel. My God, the pressure of that 35 grains is tremendous. It is only a testament to the strong construction of that gun and barrel by the manufacturer that you are able to use your hands to tell us about it! NEVER USE FFFFg POWDER IN THE BARREL FOR ANYTHING! If you insist on shooting a barrel smooth as you describe, use only 3Fg powder to do so. It is fast enough, and won't endanger you, the gun, or anyone standing around you when you fire the gun. The better method is the mechanical one described By Runner. You can use either a Round Ball, or a conical. He is also correct that by turning the ball jag a 1/4 turn, it will drive the lead further into the grooves if it seems to be getting easy to move in the barrel after a few strokes.
Another way of doing this is to use a good Stainless Steel range rod, drill a hole through a ball or bullet, then run a 10/32 machine screw with a small washer in front of the head through the ball and into the rod. Either put a cleaning patch with the honing compound impregnated in the cloth down the barrel in front of the ball, so that it wraps around the ball as would happen when loadd normally, or coat the ball or bullet liberally as you are currently doing with the compound, and then drive the ball into the barrel as it looses up with work, you can turn that machine screw a little to espand the ball or bullet a little and tighten it up for more passes with the compound. Obvously, use soft lead only, and not any alloy bullet.