Normally I would agree.However, if the sandbed is kicking up that kind of nitrate, it isn't safe to clean it with the animals in, even in small increments; they'd just have to keep water changing it back down every session. That's why I suggested moving the animals for a fairly drastic clean and then normal maintenance after they return.If corals and fish show no signs of stress, don't do anything big fast. The first thing I'd do is verify your nitrate levels with multiple test kits. If it is indeed as high as 200+, then to Eienna's point I'd slowly bring it down week by week. If everything is fine now, everything will be fine at 10% lower nitrates next week and the week after until the level is in a more normal range.
Most importantly - don't panic and don't do anything too fast.