Removing press fit bronze bushing

I have a raw water pump for a boat that has a press fit bronze bushing that goes into the back of the water pump (into a "cap" that attaches to the back of the pump). The water pumps shaft rides inside the bushing. The bore in the cap that the bushing goes into is only open on one end which is how you push the bushing in. Once the bushings in, there is no way to remove it without breaking the bushing. The stock one that came with the pump was some sort of carbon based bushing and meant to be broken with a chisel. I had no problem getting the stock one out. I installed a new one which is bronze. Once I installed it, it seemed to be warped or have some issue because the shaft didn’t ride smoothly in it. I ordered a new bushing and shaft, but now I have to remove my old bushing.

The bronze bushing does not break like the old one did. I’ve spent over an hour trying to carve out the walls of the bushing with a Dremel tool and various bits. It is slow moving, tedious and prone to error because I cannot tell when I go from carving out bronze from the bushing to the bronze in the water pump cap.

I’m looking for suggestions about how to do this better. I’ve considered using a drill press with increasing sizes of bits or perhaps just using a more appropriate choice of Dremel attachments.

Any ideas?

Update

This was very difficult to remove and especially to remove without damage. All kinds of Dremel tools (grinders, sanders, cutters, etc.) were used and while they did make "progress" on the material removed, it was impossible to tell where the bushing stopped and the housing started because they were the same material. It ended up taking a center drill to remove it. Luckily my brother owns a custom hot rod shop and has all the tools.