I have used stove top glass cleaner with excellent results on brass razors, it has just the right amount of fine abrasive and seems to lift the dirt and staining all you need is one of the green pot or tooth brush for scouring sponges with abrasive and sponge. I suggest wearing gloves when using any compounds for cleaning because if it will clean brass oxides it will over clean the skin IMO. You could test a small area on the inside or bottom of vessel to make sure, if it does not brighten up the corrosion on the inside it is just brass coating I'm thinking.
What kind of 'bit' did you use in the Dremel tool to apply the polishing compound? I assume a felt or some type of fabric.
