Invert area on OpenStreetMap

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One of my biggest frustrations with OSM is adding non-forest/wood areas to an otherwise completely tree-covered area of land.
I'd like to know if there's any way to invert the selection of say, grassland, to have everything around it be wood. Or conversely, if it's possible to place grassland on a wooded area that would cut it out, instead of just overlapping it?
This page on OSM help covers this, and gives suggestions in Potlatch, iD and JOSM.
Summarising off-site link: the mapping editors allow conversions of groups of selected polygons to convert them to relation multipolygons, and have amerge
tool to allow this in each of their editors.