Note that the 0.400 hole in the Hornady comparator has a slightly radiused mouth. This makes it read below actual numbers by a few thousandths. You have to get a good quality headspace gauge (Dave Manson, Clymer, Pacific, JGS; not Forster or other cheaper ones) to calibrate it with if you really want to learn absolute numbers. However, that's likely a waste of money from a practical standpoint. Relative numbers are normally all you need for setting up loading dies, tracking bolt lug setback, etc. As Mr. Guffey has emphasized, it is really a matter of the ammo fitting the chamber and not what SAAMI or anyone else thinks it should be. So relative numbers are just fine.
I am going to hazard a guess than when your Hornady LNL gauge reads 1.623", a good grade headspace gauge would read 1.624" or 1.625". In other words, you're getting numbers about 0.005"-0.006" below absolute. That's about how much error my copy of that gauge gives me. Figure that when you fire a round, you get 0.001" to 0.002" elastic rebound in a new case, so I suspect your chamber is just about dead on the minimum 1.630" dimension, and the reason the cases come out of the chamber the same size they went in is that rebound.
If you fired at a higher peak pressure you'd have less rebound. If you resize only the necks of your cases (just don't run them into the sizing die far enough to start squeezing the sides of the case) and reload and fire them, measuring the case shoulders each time, you'll find they gradually grow that extra one or two thousandths. Eventually, with enough firings (perhaps a half dozen; it depends how warm you load), the cases will form snuggly enough to the chamber that you start to feel light resistance closing the bolt on one. At that point your actual headspace, less gauge error, was probably reflected by the previous measurement pretty closely. That's the useful number for you to record as your reference headspace.
For break-in, Varmint Al says he likes to put some Flitz on a patch and run about 50 strokes in a new barrel (using a bore guide, I presume), then calls it broken in. That tends to clear whatever burrs or sharp edges might remain from manufacturing and lapping that encourage excess fouling. If he gets a tough dog bore (some are for no obvious reason) that fouls excessively, he repeats with JB Bore Compound (I prefer Iosso Bore Cleaner for this) to polish a little more deeply. None of this kind of polishing comes close to removing enough metal to affect the bore tolerances within the normal life expectancy of a bore. It's in the low millionths of an inch at most, and too small for a micrometer to measure. It sure saves the expense and the wear and tear on your throat from firing "break-in" shots, though.
When it comes to load development, there are lots of ideas about how best to tackle it. I always suggest reading Dan Newberry's site
for a starting point.