Thank you stevehero, for the effort you have put into figuring this out. Forgive me though, as the use of regular expressions (regex) is absolutely foreign to me and when I applied your regex it did not deliver the results I expected. Undoubtedly though, this was due to my own inability to correctly, or clearly, express my predicament to start off with. On top of this, I was most probably also applying it wrongly.
I realize now that I need to be much more careful when I describe where and what it is I need the regex to do. For instance, it is 100 albums that I need to renumber - each of which may contain any number of files. I thought I could easily adapt your supplied regex by changing some of the parameters in your format string before applying it again, but I only kept on shooting myself in the foot. It was/is great fun, however.
In the end, I gave up, and I certainly would appreciate a prod in the right direction.
Sad to report that impatience completely messed up the renaming for me. While I should have waited for your response, I opted to fool around - which I did pretty good and ended up with the mess. Now I seem to have only two options left: do it the long way or start afresh, but this time with the ALBUM field completely blank. What I still do have to start with, is the album-directory/folder already correctly named (e.g. My Album Vol. 001^100 up to My Album Vol. 100^100), but how do I transfer that to the album field, using a regular expression?