Windows Explorer fails to browse to files in *.TIBs

I have been trying, literally for days, to recover/copy files in a ATI for WD *.tib.  The TIB was created on an external USB connected to Computer1.  I need to recover them (copy them) to Computer2 due to catastrophic boot disk failure on Computer1.

Per User Guide (Help), I install ATI on Computer2, plug in the USB holding the *.TIBs, then try to use Windows Explorer to navigate to & select/copy the relevant files in the TIB from the USB to Computer2.

There are 4 incremental backup's and 1 full backup, and they are a selection of data files -- not a disk image.'

1.  In Windows Explorer I first dbl-click on the latest incremental of the series.  Acronis prompts me for the first TIB in the sequence, processes for 10-30 minutes, then prompts for the second and so on until I have selected the last incremental.  At this point the Explorer window refreshes to show the set of incremental backups available, listed by date/time.  So far, so good.

2.  I select (Open/Explore) the Date/time backup I want, then am prompted for the initial *.TIB for that series and wait about 5 mins, then am prompted to "Locate the volume with 2" then wait a longer time  before being prompted for "volume with 3"...longer wait... prompted for "volume with 4".

Now the Explorer window refreshes to show the drive letter: e.g., C:\    This takes, all told, about 1/2 hour, but I am making progress, albeit slowly.

3.  I select the drive letter and repeat the process:  ie, identify, when prompted, the first *.TIB in series, the s2, the s3 and finally the s4.  

Now I see the folders off the root:  e.g., \Users .  

4.   The above process and lengthy waits repeat each time I move down the directory structure to the folder I want to recover.  This is excruciatingly slow, but hey...maybe I will eventually recover the files!  Except that deeper in the directory structure, after the picking the final sequence TIB, the progress bar never completes--even overnight!

Yes, I have tried searching for a folder name:  e.g., Documents.   Yes I have used ATI to validate.  No joy yet.

Suggestions?