You didn't say what type of clock you have. It concerns me that the barrel bulge is so bad that it hits the next wheel. My book "Repairing French Pendulum Clocks" illustrates a procedure which you may find in other texts as well. You can make an anvil out of a length of steel rod about 1" diameter (for French barrels) or larger for others. The anvil is held horizontally in a strong vise. The barrel slips over the end of the anvil. The barrel hook (rivet) lines up with a 1/4" deep hole you drill near the end of the anvil. This allows the barrel hook to project into the hole. Now you can tap down the bulge while tightening the barrel hook at the same time. Use a small hammer for this and take care not to hit any of the barrel teeth. There may be more to your problem, such as serious problems with the barrel or the barrel hook. Sometimes a new hook has to be made. It may help in that case to go 180 degrees around the barrel and drill a new hole for the new barrel hook you have made.

also, what I used to put the barrel on to hammer down the bulge was the metal sleeve for my ollie baker spring winder, it worked very nice, has the slot for the pin already and it didn't warp the sleeve at all.