How to separate environment in Compositor without black cutouts Nice people of Blender SE.

I'm using Compositor to blur my HDRi (as suggested by others on BSE).
Cycles render engine.

However, the environment behind objects isn't rendered, there's just a black cutout.
Therefore any applied blur results in an annoying black halo around objects.  

Black halo occuring when combining blurred environment with objects.


Sure, I can render the environment separately, but it's not very practical when handling multiple scenes or animation.

Question
How can i separate the environment without these black cutouts?
I was just curious :)
Because render View Layers doubles rendering if I'm right.

You can use existing setup, just ...

add Set Alpha node and plug inverted Alpha to create transparency in BG
and use InPaint node to recreate missing environment

Note:
because of alpha antialiased edge, I added Delete/Erode node with value -1 to get rid of one pixel that did InPaint node job slightly darker