Seems work suited for JOSM utilsplugin2 plugin:

"Split area (Alt+X)

Splits a closed way/area into two closed ways/areas at two selected points or selected way. Properties of the original area are copied to the two new areas. Either select the closed way/area and two child nodes, or select the closed way/area and one way bisecting it."

https://wiki.openstreetmap.org/wiki/JOSM/Plugins/utilsplugin2#Split_area_.28Alt.2BX.29

Care to give it a try?