The real answer is one you already know, I'm sure. Present a well-sharpened tool properly. Even though willow and its cousins the poplars and cottonwood are interlocked and extremely soft grained, it can, and in my opinion should, be done that way. The one sharpening prior to the final pass is worth two grits, and on woods like maple and cherry, for instance, you spend more time trying to take out 80 grit scratches with 100 and then 100 with 150 than a beginning at 150 would do.
Help your case by not making too abrupt a transition at the bottom. Sweeping fair curves are easier to cut properly, and easier to sand, as well. A lot of relatively new turners favor almost straight-sided turnings, which can be a bugger to get right, when their frustration level would be much lower if they played it shallow and sweeping. Don't know the shape of your piece or your level of training, but good advice for anyone.
As to scrapers and willow, I couldn't ever make a scraper work properly, even on absolutely flat stuff, on wood as soft as willow. They work better on harder woods. Soft stuff crushes and tears, and the compressed areas are often revealed, as are heel bruises, when the finish is applied.
Filling with lacquer or shellac are death on sandpaper, but they do keep you from getting some tearout and heel crush, so you might want to try it, realizing that with wood as absorbent as willow, you might limit your choice of finish.