I found exactly the same thing, a piece taken from the base stone seems not to be the best tomonagura, even tho that practice have been a "truth" for some time.
I guess what we are looking for is just the perfect mix of very fine abrasive particles together with something that will buffer them and cushion the steel against the stone.

I for one haven't tried "tons of them", i wish... But hey, I'm only a stones throw away!