I have made good use of John K Jordan's advice about negative rake scrapers and scraping the stationary bowl with small hand-held scrapers. He also led me to get a thick scraper from Stewart Macdonald which is quite nice. It's easy to grind standard card scrapers to any curve needed and put a hook on with a burnisher.
A great advantage of scraping and sanding a stationary turning is that the stock removal can take place exactly where needed. When cleaning up a rough surface that is rotating, more material is removed from side grain areas whereas the worst problems (tearout) are usually in the transition areas between side and end grain. That can lead to the work getting out of round and the process taking longer than if the local problems are smoothed and faired into the surrounding areas. I don't do that much sanding with the piece turning except when getting into corners, beads and the like. I do use scrapers while turning to fair the overall shape if I can't quite get there with a gouge.