I never did truly understand "exactly" what it was about how I was using variables that was the problem but I found a work around, so to speak.

First if you want to use a variable to hold a "bad" file name, or one with unusual characters in it, to be used with the cp command -- then process the filename the minimum amount possible. I was processing the file name to create a new name, then I had to process it some more to undo the first processing so I could get the original name back. Bad idea, something happened to the filename while doing all that processing and I could never get it back to exactly what it was before... So I set out to minimize the processing of the filename to be used in the variable used to copy the old filename to the new filename.

Second, bash does its own processing of special characters and spaces when the cp command is run. Do not try to help it by adding escape characters (backslashes) to the variable. You have to deliver the name to the variable "exactly" as it appears when you use ls to display it. Then if the variable is quoted with double quotes, then bash can properly process it -- no matter what characters are in the file name.

Even though you can type the filename in by hand and add backslashes to the name and when you run the cp command from the script, it will work -- that ability will not transfer to a variable. Putting that same text with backslashes into a variable does not work because the variable does some processing "before or as" it expands the variable when the cp command is run. That "extra" processing produces something that is different than what was put in the variable, usually it adds backslashes and when it does, it does not match the "real" filename and can not copy it to the new filename.

Here is how I was originally processing the filenames. I was creating a list of filenames and storing them as a variable. Because the variable "fed" a for loop, I had to remove any spaces before I used the variable (for loops will not work with spaces in the filenames). I created the "filename list" variable and converted the spaces to % at the same time. I then separated the filenames into the basename and extension and stored them in variables. When I finished I reassembled this to get the original filename's basename and extension and removed the %s that I had inserted previously

This was too much processing. I ignored the KISS rule. The final cure was use the entire original filename with the % added -- as provided by the for loop -- instead of breaking it into basename and extension and having to reassemble all that back into the original file name. This allowed me to use the original filename with no processing other than removing the % symbol which I did at the same time I reassigned it to the final variable used by the cp command. Then all I had to do was quote the variable and everything worked.

My filename repair script works perfectly now and can repair filenames with leading and trailing spaces, backslashes, single quotes and any other characters that I have tried so far except the % symbol. There are two problems with % in the filename. When they are assigned to the variable storing the filenames bash turned % into %%, then the script turned all spaces into % and things went downhill from there. I decided to leave things alone and not try to process files with % in them, (files with % in them are very rare anyway).

I hope this makes sense, and can help someone in the future.

Thanks for everyone's help.