I recently helped a friend Dremel off the extra leash bit of his knock-off Peak Design Leash. This gave me the opportunity to document the modification (I had Dremeled mine off years ago). Please ignore any material differences (a genuine Peak Design Leash is much better).
The little plastic bit that makes the strap able to wrap around one end to your belt, wrist or other object is also an object that rubs against your shoulder when using the Leash as a sling strap.
I Dremel mine off very carefully (the plastic is dense).
And now it slides over my shoulder much easier.
Viola! Now it is like a SlideMINI.