Taa-daa! :) I`m proudly present my UV-islands copy-paste plug-in for Blender.
Demo video.

Link for add-on itself will be added soon.
Also I`ve opened bug report about strange behaviour of island select here.
From Blender community site.
Stacking of symmetrical geometry - often times geometry that is exactly the same we will want to use the same image/texture data to save memory however, aligning the uv islands so they exactly overlap can be tedious. This would allow automatic alignment of UV islands for mirrored/symmetrical geometry. 

P.S. (Update) Due to some internal data organization in Blender this add-on works well on closed seams only. It means that UV island must have all vertex unique and no vertex split up.  In UV editor with sticky selection mode set to shared vertex no vertex should have pair. Add-on can be used in real work but with previous restrictions. So it needs additional design changes for open seams. And work in progress...

P.S.S. For those who would like to use and test it in it's current state, installation instructions (in English) can be found here. Also installation instructions in Russian.