First, thanks to everyone that advised me. Regarding my battleshield cap in Sins of a Solar Empire: all I can say is "duh". I thought I had researched that second level, but I hadn't.
As for Steam . . .
The premise behind how Steam handles DRM is that you can install Steam and all the games on your account on multiple systems, but that you can only log on to Steam on one system. This makes perfect sense: my license says one user can run the game. In other words, if my son is playing Plants vs. Zombies on one system, it's fine to restrict me from playing Plants vs. Zombies on another system at the same time. The problem I had is that this restricts ALL the games I have purchased using Steam. If my son is playing Plants vs. Zombies, I can't play Empire: Total War at the same time. This makes no sense.
It turns out that this isn't quite so bad. I ran an experiment where I started up Plants vs. Zombies on one system and then started up Steam on another. On the first system, I got the message box saying Steam was disconnected. But, I noticed that Plants vs. Zombies was still there, minimized. I was able to happily continue playing Plants vs. Zombies after that. Cool!
This does bring something to mind: because this involves Steam logging off, does this mean that I can't run, say, Left 4 Dead on one system while one of my sons is playing Team Fortress 2 on another? This warrants an experiment, another time.