Lost My Mind At the Range
A couple months ago I went to the range to sight my carbine. By the time I had it lined up, the aperture was over against the sight frame but basically centered on the receiver - in other words, the sight base was pushed over too far. Later I marked everything, knocked the sight base loose and reset it with Loctite in the correct position. Today I go back to the range expecting to maybe make minor adjustments with the windage screw, and it was shooting way right. I couldn't figure what happened. I finally got it lined up but the aperture was all the way over again. I guessed I had made a mistake somewhere and brought it home. Later, putting it away, I took another look at the sight and saw what had happened - the sight base, although appearing to be solidly fixed, had shifted in the receiver. It won't move by hand, but must have been jarred on the way to the range or maybe it moved from recoil. This time I use RED Loctite!
The problem isn't the sight
it is the sum total of the manufacturing errors that causes these things to not line up like some weapons. The barrel could be bent, offset in the receiver, the index marks wrong, any number of little things. My original Winchester has lots of these things and when you look down the barrel, not much lines up. It does have the factory installed adjustable sight lined up close to center, but it still isn't right to the naked eye, but shoots great.
When I said "You might not ever get it right" I mean if you put a nice gob of red on that sight and it happens to be clean and fresh, then you might be stuck right there and never get it off. Just because the rear sight is centered doesn't mean that it will work. In WB it points out that large numbers of barrels were bent when they arrived from the manufacturer, so having to do radical sight adjustments isn't an uncommon thing.
I've never had much luck preaching to the choir
I can definitely let it go. The red Loktite is just a bear to get off, that was my only concern. You've obviously got it right.
Now can I impress you with a little historical background on the rare Singer carbines?