Well, I contacted the vendor Simon Schild at Simon3D and he was very helpful, sending me a new file (one of the finger digits didn't have a dial in the parameters) and making some suggestions.  He said to turn Limits on and that solved most of the problems.  I can now copy and paste the walk cycle and the feet remain on the ground - no more drifting or dipping below ground.

However, when I made an animation file and stored it as a pose, when I applied it to the figure the feet came off again.  Oh, well, at least the copy and paste lets me get where I need to for now.

Simon mentioned that it might be a problem with Poser 7.  All I got, so I'll never know.