I dropped my LTR into an extra PSS stock I had.  It looked like shit.  The forearm almost came to the end of the barrel (well, about 6 inches away), and the channel was way to large.  All in all, I'd strongly suggest against it.

It wouldn't hurt my feelings one bit to cut back a factory Remington barrel.  If it shot good before, I'd bet it would still shoot good after cutting it back (assuming you don't do it with a pipe cutter!).  Saving a factory barrel for anything other than muzzle brakes and mock ups seems crazy to me.  I'm not going to spend hours getting a receiver into shape just to put a box stock factory hammer forged barrel back on it.  Cut it to how you want.  If it doesn't work, or you shoot it out in 5000rds, then get a high end barrel.

Of course, this is all under the assumption that if you continue to use the factory barrel, all you're going to do is cut it back (without removing it from the receiver).  And, if you were going with a high end barrel you do the full blueprint, oversized lug, bedding, and the whole nine yards.

I really like 20-22" on little guns like that.  Most people think I'm crazy, but I'd probably cut it to 20" and add a Vortx or Phantom (you have to open it up a bit, but that's not hard to do).  I was going to thread my LTR for one, but have taken so much crap about it, I'll have to do it on the sly.