@Mous It (kinda) exists actually.
Look for Shadowrun: Anarchy. It's a total stripped down ruleset that's a lot easier to throw together, is streamlined for storytelling rather than finicky details, and feels positively FATE-like.
The long-running Shadowrun campaign I'm in has gone from 4th, to 5th, to Anarchy, and have enjoyed Anarchy quite a bit. It's so much smoother--for one, the GM doesn't have to pause the game every 5 minutes to look up mechanics. :-}
@emanate How well does it handle combot flow between physical, matrix, and astral rounds? That was the biggest thing that bogged my group down to the point that we had to stop playing.