Well, I got it figured out.

Apparently, somewhere along the line I created (or something created)
a "custom catalog" which was messing me up.

To find it, I went into the Control Center, then clicked on Configuration,
then Platforms.

At the bottom of this page is a section called "Custom Target Platforms".
Inside there was on called "oes-linux-i586". I don't know what this was,
but it was making my life bad. To make matters worse, I couldn't delete
it, or disable it.

But what it WOULD let me do was to change everything about it. I renamed
it, and changed everything inside of it. Once I did that and saved it, I
removed my servers from the Devices list inside the Control Center, went
to the console on each of the agent servers and ran zlm-uninstall, and
then reinstalled it. Now they are working like they should.

Hope this is of some use to someone. Thanks to everyone's suggestions
along the way....