Bolt action 5.7x28 micro action.
Get out of my head!
I was thinking on maybe an older Kimber 82/84 action or a Ruger 77/22 hornet action for this.....
It needs to be light maybe 4-5 pounds finished weight too!
Armscor makes a 22TCM carbine that is about as similar to this idea as I have found, but it has a 2x4 for a stock and is pretty heavy and clunky. Also 22TCM ammo is harder to find and more expensive.