I indicated in my prior post, that I would provide an update for the benefit of others.
After working with them for a few days, tech support turned out to be a mixed bag. I think they tried to help me, but nothing they suggested actually resolved the problem. However, I was able to solve the problem on my own.
There were three sparse bundle disk images, created by disk utility, that contained important files that had not yet been backed up. There were also four additional sparse bundle disk images that had been backed up. While all seven of these appeared to have been restored, none of them would open.
From my observations of working sparse bundle disk images, a normal sparse bundle disk image is really a folder, not a file. (you can peak inside by right-clicking, or control clicking on it.) Inside of it is another folder named "bands" which contains the files that get combined to make the actual disk image, when you open this. Remember when modems were slow, and we segmented disk images? Well think of the band files as something like disk image segments.
There is also a zero-size file named token, which aside from the obvious suggestions of it's name, I have no idea how it is used. And there is an Info.plist and an Info.bckup. In all of the examples that I looked at Info.bckup and info.plist were identical. It appears that the information in this file is important enough that Apple wanted there to be a backup.
In all of the seven sparse bundle disk images restored by Stellar Phoenix Data Recovery, the tolken, info.plist and info.bckup files were missing. I created a new sparse bundle disk image having the same characteristics, and I copied the files that were missing into the recovered sparse bundle disk images. After doing that, they would open. I'm not sure that it was necessary, but to feel extra good, I repaired them. (with Disk Utility and Disk Warrior)
Since the info.plist file contains information about the maximum size, and band-size, I'm not sure if just any would have worked. But I had created all of them the same way and remembered so I could create an empty one having the same properties.
At this point, my assumption was that Stellar Phoenix Data recovery simply filtered out plists and files of zero length. After all, it had successfully recovered many gigabytes of other files. And they had the right names, and were in the right folders.
In an effort to test that theory, I took an external firewire drive, zeroed it and made a small partition. I then put data on it, including some sparse bundle disk images. Lastly, I used disk utility to do a simple erase.
However, this time Stellar Phoenix recovered almost nothing. And I have not a clue why.
So, my take is that sometimes this program will do an amazing job of recovery. It will recover files with the right names and in the right folders which is far superior to what most other utilities will do. But in other cases, you may hit a dry well.
If Stellar can improve the consistency of success, and make a few things clearer, they may have a winner. I'd say it is still worth giving it a try though, as the other recovery products tend to give you a set of generic folders with files named picture1.jpg, picture2.jpg…etc. having lost all of the original meta data.