Here are some pictures showing how many of the Lyman sights are held together, the elevation nut has a flange on the bottom which is held in by a ring that is crimped in place. I think what is happening is the stem get bottomed out and then the adjusting nut is turned more which loosens the crimp. Some Lyman's came with small pins in the bottom of the stem that were to be cut to size as a stop for the low setting, with these they will bottom out and still appear like they should adjust lower.
To tighten this you will have to tap around the crimp, support in in a way so you are not putting any force on the hinge screws and use brass or another soft metal. Don't over do it because it still has to turn. (PS, warning, I have not actually done this!)
The old patent shows a square section ring, the rings in the later sights I have seen are triangular. I had a sight with the threads on the post stripped out that I made into a cut-away.
Here's one that was taken apart by prying the crimp open on one end, notice that it also was pried out to open it, that is another thing to look for -
The probable reason they never made a loop spring type sight for the 1899's is due to the limited stem length..
These short Lyman's hinge on the ends of screws, this allows for longer stems in short sights, similar to their sights for the Remington pump rifles and the Winchester 61 . The looped spring type limits the length of the stem and would not be practical in short sights.
The locking type have a relief hole in the hinge on the shorter versions so they allow a longer stem length than the loop spring type can and for the 1899's they have longer bases setting them back so they can be made taller over all.