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Where to get shims for the barrel insert?

Triggershims.com. $14, including shipping, for a three pack. The most popular pack is 1 ea of 0.001", 0.0015", and 0.002". You can order any three thicknesses you want for the same price, though, and it all depends on how sloppy the fit is whether you would need thicker. Joe Carlos has some good videos on how he does it, and some people will use a bedding compound instead of or in conjunction with shims.

https://triggershims.com/ar_15_shims.php#S23
ETA: you have to scroll down the page a ways from where that link takes you.
 
As mentioned, it will depend on how loose the fit is. Its kind of ironic in that, the more loose the fit is, the easier it is to shim, because you can use thicker stock. Trying to use 1/1000 shim material is a real exercise in patience. Once you apply the loctite, everything is going to want to slide around and the shim material is going to want to crumble and once you get it all together, youre gonna be wondering if everything is true.

I'd just spend the $60 and order a receiver from Bking (I think it is) that is meant to be thermal fit. I think they call it they're mod 1 receiver. If the fit is just a slip fit, but isn't too loose, I'd just bed the extension with some green loctite (620 if I remember right) and just be done with it.