I will be interested in this too.

The only way I know of is very "mandraulic". As follows.

Goto Active Listings View.

Click the Customize link (top right-ish)

Check the box for "Available Quantity". You can move it to display in whatever position you want.

Click Apply

Now your quantity available will be displayed on your active listings.

Then if you click "show variations" over on the left in the title column they will expand so you can see all your variation quantities.

Now... If there was some way to download this view into a CSV file so you could get it into Excel or similar then you could do all kinds of searching on it.