Driving them out with a simple punch won't be easy and you will likely scar up the insertion bore on the machine. You need to shrink the OD of the worn bushing first before trying to remove it if you want to keep the bore clean and make your life easier.
Steel bushings can normally be welded inside the inner bore and allowed to cool. This will shrink the bushing and allow it to be driven out easier. Weld a full circle inside the bushing assuming enough is still left of it to accept a weld bead. Rod type really does not matter as long as you can put down a bead. Sometimes I also use an AirArc, plasma cutter, torches or Sawzall to cut a relief line down the bushing to shrink it. I also custom grind punches to split and curl back the softer bronze bushings or very thin bushings. DO NOT scar up the interior bore of the machine where the bushing is driven into. A cylinder hone will clean up any scale and light high spots prior to installation of new bushings.
I usually custom cut bushing driving tools on my lathe for the installation of the new bushings. If you have access to a lathe, do that. Your bushings will be installed cleanly without deformity if you have the correct tools. I normally cut them from solid stock, cut a driving shoulder that will do the actual driving force and center bore it so that I can pull it in with a piece of 5/8 or 3/4 all thread from the other side. This also assures proper alignment when starting the drive in. Weld a nut on the outer end of the all thread so you can drive it in with a sledge if the pulling does not work on its own.
Chill the new bushings before trying to insert to reduce the OD and make insertion easier. If liquid nitrogen or dry ice is available, that is safest. Me, I normally use liquid propane as it is usually the only cold stuff I have around the shop. Propane is NOT safe but then neither am I. DO NOT use that anywhere near people, buildings, engines, etc. Use your head before messing with flammables.
Maybe if you need some bushing practice you can help me with the Menzi next winter! I've forgotten how many bushings go in this thing but I did replace about 12-15 on one front steering knuckle this past spring. That did not include the front or rear of the leg. It likely has well over 100 replaceable bushings, mostly bronze.
