It "works", but there are some potential issues...
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Neck thickness: Necking down makes the necks thicker, and some brass moves in the process. I've got a Shilen barrel on one of my .270(s) that used their .305" neck reamer. Sizing brass down, such as being described, would force me into neck turning. Regular Win .270 Brass is right at .303" in the neck when loaded. If you have a tight neck, you'll need to neck turn.
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Necking Down will move some brass: It probably won't be a huge issue going from .308 to .277 (actually .002" - .004" under for neck tension should be the result), but you're almost 'wildcatting' here. As with necking down in other wildcats, you'll be moving brass. The real issue here is avoiding doughnuts at the neck-shoulder junction. Not all doughnuts are good for you
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OAL, and Neck Length: The .270 spec is longer than the .30-06, mainly in the neck. You'll be several thousandths short of the 'in-spec' neck.
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Using short necked brass: RCMODEL must have been reading, and I've come across what he mentioned in stuff by Ken Waters and Dunlap. This operation was a classic case of 'use in moderation'. The short neck is supposed to cause wear in the neck area of a in spec chamber. Thhis will lead to an area that is hard to clean, and if done a lot will erode. In some cases the erosion is reported to cause the neck to flare after firing, making extraction difficult.
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The headstamp still says .30-06: It will be a PITA if these get mixed in your .30-06 brass.
It works, but it is less than ideal.
IMO, and just my $.02 here...the final product is slightly flawed. Life's too short, buy a bag or two of brass, unless you're just going to get through a hunting season.