Would the outlet from your dehumidifier work to circulate dry air around the area?
It outlets at the top so possibly not but worth a go
Or position it to draw air in from one side of the alcove and expel into the room. Again, it may not be workable with a top exit
http://www.greenbuilding.co.uk/GBF_Forum/discussion/2325/condensation-and-fitted-wardrobes
@rogan started
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Would the outlet from your dehumidifier work to circulate dry air around the area?