After piecing together results from various users I arrived at the following:
The Droid3 Moto Rooter does work for most people. If you did not "unroot" before upgrading to the new VZ Ginger ROM, you may have trouble.
Basically, the existing "su" and "busybox" that were installed and kept during your upgrade (i.e. from Z4Root on Froyo) cause the new root to fail to install.
What follows is certainly NOT "one click root"...you need some exp with command lines, etc...please do not attempt this unless you're confident in what you're doing.
So I stepped through the actual lines of the script, including letting the phone reboot between the comments "Stage 1" and "Stage 2", and after "Stage 2" was complete (I let it reboot again).
When the phone came back, I went into the shell and followed the instructions listed at the bottom of his page for the Droid X. (When you try "adb shell", you should get a # prompt, not the $ prompt. This is an indicator that you'll be able to remount the fs to perform your fixups.)
Basically remount the filesystem as rw, and remove all traces of existing "su" and "busybox" binaries from the phone. THEN you can run the commands he lists in "Stage 3" to "push" the new versions of the files to the phone and change their permissions.
When that was complete, all my root-required apps (like TiBackup and SetCPU) were happy!
Hope this helps. As always, there's a lot of info out there, and it's sometimes hard to piece it together.
-AJ