You shouldn't cut through the grain lines at all on the back of a white wood bow at all. Peel or scrape the bark off until you get to the outermost growth ring and no farther. If you take an already stressed high crown and you violate the growth ring on the back it's asking for failure without another backing on it. The rawhide will help keep it together if you did nick it a little here and there but it's preferable to have it clean in either case.
If all I had were high crowned staves, I would at least experiment with building them backwards. Split it right down the middle, sand out the surface where the split was with coarse to finer sandpaper until it's as smooth as you can get it to be, back that in rawhide and tiller it from the side that is usually the back. You would end up with a flat back and belly after tillering it. The grain would run vertical end to end, seems violated but it can still work for a self bow if done correctly, backing it in rawhide will help ensure it stays together and is probably the safe thing to do for a bow built in this manner.
A scraper is a simple tool, lots of things made of steel can be made into a scraper. A knife, half a pair of scissors, a rectangle cut out of an old saw blade, chainsaw bar, the main thing is that it scrapes or shaves off just a little bit of wood every time you run it along the limb. With a cabinet scraper you put a small burr on it's edge and you end up with nice little shaved curls of wood and a smoother surface than you get with sanding. Relatively inexpensive and easy to make yourself, if you make one look up a "burnishing jig" to make putting a burr on it easier. I wouldn't abuse my draw knife by using it as a scraper, two very different tools with very different purposes.
You should always follow the grain whatever direction it seems to take. If you split a small tree the split will follow the grain. Your bow should follow the grain end to end of the stave if the stave snakes around you must follow the grain around these bends.
You've been given a lot of really good advice in this thread, hope the next one turns out well. After you get the next one down to being on a long sting on the tillering tree, take some pictures of the early bend and make a thread. State your thoughts on where you think wood needs to be removed, the folks here will either concur or tell you otherwise. After getting it to brace post pictures in that thread and do the same thing. Taking the tiller slow taking pictures and asking the folks here about it before you go too far to fix things will probably help your chances.
