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Is it possible to free float a 10/22 barrel with the way the V-Block attaches to hold the barrel in?
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As long as the V-block is supported (or a couple of inches of barrel in front of the V-block), then yes. Stocks with pillar beds help a lot.
The original 10/22 design with the single action screw is definitely a weakness. But the pressure imparted to the barrel from the stock (particularly the pencil barrel) is a weakness, too. With a regular wood stock, I can literally change the POI on my 10/22 by inches at 100yds just by the way I place the rifle on the bags. Maybe the Magpul polymer stock doesn't flex/impart as much pressure on the barrel, but a little goes a long way on a standard Ruger barrel.
One remedy is to free-float and bed. Another thing that helps is to pin the rear of the receiver. Some aftermarket receivers actually have a rear tang that is screwed and anchored into the stock. This eliminates the teeter-totter effect of the free-float and takes a lot of stress off the front action screw. Those aftermarket receivers usually cost as much or more as a standard 10/22 all by themselves, too.
Another method is to remove the buffer and replace it with a barrel bolt (aka sex bolt) like
these or similar 1/4" piece of stock that is bedded into holes drilled into the sides of the stock. You take 2 and an all-thread and trim down to fit...it's cheaper than a Kidd Action but a more labor-intensive project and isn't as aesthetically pleasing; but it gets the job done.
The cross-bolt look kinda like this when you're done.
I===I with the two ends anchored into the stock and the barrels of the bolts serving as the buffer.
Some product pictures of the X-22 stock all by itself with an overhead shot of the barrel channel would help answer a lot of questions.
A pic of the reversible barrel-tray would be great, too.