Blender export paper mode

Allright, I think you’re using this Export Paper Model addon:

I don’t have any experience with this addon but I read briefly.
Those red edges displayed are marked as seam and blue edges are marked as sharp. Try to select all edges in edit mode and hit Ctrl+E > Clear Seam and Clear Sharp. Then try exporting again, this will produce an island that is connected. Is that what you’re looking for?