The plan was to be farther along with this restoration, but I think I heard a saying about the best laid plans...
I came away from this exploratory surgery with a fairly good idea of what was causing the wayward keytops. Unfortunately, the solution wasn't the button I found deep in the bowels of the typewriter. That would have been too easy.
It was something far more interesting; a pivot point.
The keytop arms of this particular typewriter are very long. The extend all the way into the back of the frame where they pivot. I think this is something well-known to Underwoods. Each bar has a small tab of metal that engages with a comb/pivot plane. An extended "Z" bar-like piece covers these tabs and the pivot comb allowing the arms to stay in place, but also move freely. Small springs add some push to the tops and keep everything aligned. In the picture below, I have removed the retaining bar for ease of viewing.
On this typer, several of the arms had worked their way out of the pivot comb. Their conspicuous absence can be noted above. This small change rendered the typewriter unusable. Here is a better view of the absent key bars:
The metal tabs were intact on both bars. I imagine if they were actually broken I would have a whole set of other problems, but they look good. The loose retaining bar might have contributed to them working out of their locations.
To fix I just formed the metal "Z" a little so there would be a tighter fit. I have yet to reinstall it, but I was thinking that oiling this point might make more trouble than it solves. There is no sign that oil was ever applied here and adding it at this juncture might cause the pivot points work loose even easier.
I am also fairly confident that the springs that are on the underside of the bars are important to alignment because they keep the keytop bar tabs pushed up firmly against the pivot comb. I have a few extras from a very bad donor machine.
I am getting closer to some of the more fun stuff, but without a solid working mechanism all the rest would just be window dressing.