Hi, I am fairly new to bushing clocks, I've only done two successfully so far. Happy they worked out great. But, I am wondering what to do when the hole you have to bush already has a bushing in it. Do you recommend punching out the old bushing and replace or do you recommend cutting out the old bushing using my Bergeon cutting tool for the size bushing I need? No pictures to show since this is a hypothetical question.
There are several things to consider in the case you describe. You say you are new to bushing clocks, so just in case you have not discovered this, what many beginners perceive to be bushings are not bushings at all, but just stamped impressions around the pivot hole. For these, I prefer the Bergeon bushings because their larger outside diameter will often completely cover the original impression and (to me ) just looks better.
Locating the exact center of the original pivot hole
is very important. If the pivot hole already has a bushing that is worn out and you try to locate off of the worn bushing, any error in the original bushing location is added to any error in your own determination of the center. You also have no way to know how the worn bushing as instilled. I cannot recommend attempting to bush a worn bushing, it needs to be replaced. You simply cannot replace a worn KWM bushing with another bushing that will fit the pivot hole without compromising the minimum recommended wall thickness of the bushings.
As others have stated, if the worn bushing is a standard bushing, knock it out and if it seems to be tight, just replace it with the same size new bushing. Otherwise knock out the old bushing, locate the center and ream for a larger bushing that has enough wall thickness to safely be reamed for the correct size bushing for the pivot. Bergeon bushings are especially well suited for the "outer bushing".
When doing a new bushing in a bushing I select bushings that are longer than the plate thickness and leave them a little proud on both sides, then trim them flush. It can then be difficult to even see that there are two bushings.