some solid stamps i always have that issue with. and I have done the things you are saying. I have tried a couple of things to get over it, either a sponge (like a makeup sponge that I gently use to dab more ink on the finished image to even out the color) or direct coloring on top of the image. Sometimes I wonder if the stamp is just not mounted well to the block.
Is it completely bare in one spot or the ink is just not completely even when you stamp?
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