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Hmmm I would drop the BBW and replace it with the DT... or the other way around, but I wouldn't buy both unless you just want them...
They are pretty comparable stones IMHO, both can cut with slurry...

I would leave the Barber's Hone out of the equation for now,,

Bevel set = King and it is a gentle cutter

Sharpening = BBW with slurry

Polishing = BBW with water

Finishing = PHIG