I only use a band saw to get the rough shape of the bow. Just to eliminate the bulk of the excess wood. After that I use a rasp to get to floor tiller and after I get about 4" of tip movement I switch to a long string. Be sure your limbs are bending evenly during floor tiller. I use a draw knife only to remove the bark and sapwood. In whitewoods I don't use a draw knife. Just peel the bark, reduce the excess wood with the band saw and rasp to floor tiller stage. Once I get any stave past floor tiller I use only a scraper to tiller the bow. When I'm sure the tiller is good and the string tracks correctly I shape the handle and tips.
After I sure the tiller is right and I have shot 50 to 100 arrows through the bow I will use sand paper to remove the tool marks.