...it does power and run the berry.
That being said and as you eluded to, the 8100 battery cover that comes with it does not fit the 8130. And it's not just because the cut-outs for the camera do not match. The tabs on the cover that interlock with the case are not in the same location.
I have used my 8130 with the 2600mAh battery to watch videos on long airline flights. You just have to leave it's backside open (kind of like a hospital gown)
I have not seen any skins or cases that would work with the 8130/2600mAh battery combination.
Please post here if you find something that works. I would jump on it in a flash!
Hope this helps.
Two Mike Romeo