How can I make a vertical panel not overlap the bottom panel on my screen? I've seen screenshots of KDE4 panels that only take up 90% of the width of the screen, but I can't find an option that would let me resize a panel's length.

I'm running Mandriva 2009 x86_64 with KDE 4.1.2

See [thread=6902]this thread[/thread] on how to configure your panel. Configuring the width is not easy to recognize but it is there
Watch the arrows on both sides when configuring.

I tried checking this in my Mandriva 2009 VM inside VirtualBox and was able to do it but now that I've booted into a full install of Mandriva 2009 x86_64 on a separate partition, the little triangles at the edges of the panel don't appear.

Strange thing is that in the VM, the buttons to left/center/right align the panel look much the same as in a typical word processor, but in my full 2009 x86_64 partition, this functionality is only under a More Settings button with three larger buttons under panel alignment in a drop-down menu. I could have sworn that both installations use KDE 4.1.2, but I'm obviously under some kind of delusion or I'm not comparing the same package names (there's so many KDE packages that I just look for a whole bunch of 4.1.2 packages and assume that's the version I'm using).

So, given that my x86_64 Mandriva installation has the latest updates, it looks like the panel shrinking functionality has been removed now?

That sounds like a backport to me. Can you post a screenshot of your panel in configuration mode?