I agree, as a long term solution doing DC > AC > DC stepping is very wasteful. Though I can see the appeal of the product in other use cases.
They don't seem to have that model in the UK either. I should sign up to Amazon.co.jp for you to use shouldn't I
The for you the most economic route would be to walk the dead battery into Akihabara and have someone re-cell it. They're almost certainly just commodity 18650's. Should cost peanuts!