Years ago (1972)I found some toothpaste from Denmark, I think, called SMIKI. It was a light grey/opaque sort of gel and there was no hint of mint at all - probably baking soda more than anything.
My first try was Yuck! But it removed all the gunge from everywhere without hard scrubbing and I didn't mind the flavour.
But I haven't found anything like it since.
Robyn