Great thread and pictures Msaternus.
I heard that you can take off grips without having to cut through them with a blade using an air compressor. Is that true? If it is, that could be easier and you would conserve the old grips. Sometimes you just want to regrip the clubs with specific grips that you like and have to sacrifice the original grips, that are new in that case.
I use the biggest hypodermic I can find with as thick a needle as possible to try to save old grips. I just inject some kerosene or gasoline near the butt end, about a hand width from the butt, make a bubble and work the bubble up, down and around until the gas or kerosene flows out onto the shaft. You need to get the needle against the metal and inject carefully to avoid a mess. The bigger the hypo, the easier to inject. Once the gas or kerosene gets out onto the shaft, the grip comes off easily. It's a lot easier if there are two of you or you have a bench vise. An old rag kept handy can save you from a mess too. It doesn't take long to figure out how big a bubble to make.
Grips that are moved from one club to another come out a bit bigger and will likely need a layer or two more tape or need to be stretched on the shaft to maintain a reasonably firm feel for the player.