Longtime user with quite a bit of experience with the Gallery feature.
There is a way to add images from the Media Library using "includes" and the image ID number. You can read about it at the bottom of the Gallery Support doc and in the FAQ I've written up on the feature.
If you need a demo, http://agallerydemo.wordpress.com/2011/03/15/include-from-media-library-gallery/ As you can see, this works well for a limited number of photos. But as you have tens of photos in each Gallery post, that is the reason I recommended simply reuploading your file again with each Gallery. Your file is all of 110K in size, so it won't be eating up your 3GB of upload space even if reused.
If it were me, I'd add a widget since it is then present on all posts and pages where the sidebar shows.
I believe that TPTB are well aware of the limitations of Media handling in the current iteration and for the past 3 years they've talked about revamping it. Hopefully one day they'll get to it.