This is what I know so far.
With no access hard drive access I speculated my quickest choice was to another attempt making a disk image of the whole drive with Disk Utility. I selected the whole partitioned drive and it worked to make a disk image.
I can't say if I didn't have the root user initiated, via Director Utility, when it failed before but I did have it enabled the second time. I successfully made a disk image, which took forever. I was able to successfully verify and open the disk image file on a new hard drive. The initial verification was also brutal but less than overnight. Once opened, the disk image contents were untouchable, uncopyable and immoveable by Finder and with the Root User enabled.
Using Terminal I found CP couldn't touch it. SUDO CP had access but it flagged symbolic link errors.
What worked to move the Time Machine files out of the disk image was sudo cp -RP which handled the files without errors.
However, using BASH to copy files seems to take FOREVER.
Through further research I discovered rsync.
Along the way, I discovered iTerm which is a nice terminal emulator.
Using iTerm and rsync I am now finishing my movement of Time Machine files. I believe that Time Machine compresses the files somehow because the footprint is much, much larger than what is was before. The rsync command line I used to move the Time Machine files from another hard drive into a disk image and back out onto another hard drive was:
rsync -avzdlkp --compare-dest --stats --progress
If you look up rsync you can see why it is taking so long because I have a bunch of options and safe guards to keep the transfer OCDed. When this is all done, I will re-start Time Machine and see if all this effort produces a working folder. and post my findings.
I speculate that with rsync I may have been able to move the files off the faulty hard drive but the risk of total failure was higher. Even though it may have been possible if I had known, I think a disk image is much faster to make when you have a crippled six month old Seagate desk top Backup Plus, than rsync or sudo cp is to copy and verify files using terminal.