What are the consequences of not completely removing the old polyurethane?
I have tried in the past to use a belt sander. Now I rent a drum sander and finish close to the walls with a belt sander. The preparation is very important for a quality job. Any old poly left may appear yellow when a new coat is applied. If using a oil finish it will be an absolute must to remove the poly because the poly will not penetrate even a thin coat of poly. I know you don't want to restart with a drum but it will look much better and you can use a finer belt Providing a better finish in the long run.