If your barrel is properly headspaced now then screwing the barrel in is not recomended nor will you gain much from it. Typically the breach face is only .005 to .010 away from the bolt head. This is all the space you have to work with and you still need a few thousands so the bolt will operate freely so you are really only working with .002 to .008. 3/16" is .1875 so as you can see moving the barrel .002 to .008 would be like pissing in the ocean. Longer bullets will get you closer and if you are really serious about it then setting the barrel back (have the breach face trimmed and rechambered) would be an option.
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