OK, so I'll answer my own question, with many thanks to Ron (username WOLF) for his research and advice on this.
The commands have been removed from DarkBasic Pro and there isn't anything that looks remotely like the "future enhancements" that were added as replacements.
You can, however, use Dark Basic Classic as a WYSIWYG editor to create custom animations for your .X models and then play them back in Dark Basic Pro or any other language/program that understands the .X format.
The output of the old SAVE OBJECT ANIMATION command is basically .X data with the object itself removed -- it's the animation template by itself. Since the APPEND ANIMATION commands are gone in Pro it's pretty useless now. And APPEND OBJECT in Pro barfs on a .X file with just animation data -- it seems to want the object in there as well.
So I cheated. I ran my DBC program that lets me arrange a model's limbs using the keyboard, and takes a "snapshot" as a keyframe, over and over until I save the animation to disk. This is essentially the Sample code for the DBC help example on the APPEND ANIMATION command, with some extra code put in that lets me select a limb and waggle it it back and forth, a command to rotate the model and zoom in/out, etc. It's either #26 or #28 in the DBC examples folder.
Then I opened up the original model's .X file in Notepad, and the animation data file I've just created (also in Notepad), and found the location within the model's file where animation data would go if there had been any (three curly brackets from the end of the file), and pasted the animation data. Oh yeah, I made a backup of my original model first.
Last, I had to remove a tag from the animation data, similar to "xof 0303txt 0032". There's already one at the beginning of the model file and DirectX didn't seem happy having another one in the animation section.
Works like a charm. This pack of 24 human characters I purchased from Geo-Metrics, "jointed but no animation" are starting to come to life now, using Notepad and a crude but effective tool written in DBC that is still far easier to understand than the convoluted interfaces in GameSpace, Milkshape, etc.
Notepad -- the ultimate 3D animation tool.