While your approach is possible it seems like a lot of work over an entire collection.
I have a small action which you could run over your entire collection which would fix them all at once preserving the form of a name which starts with an article.
Yate has the concept of an Artist list which can be filled manually, automatically or on-the-fly by editing fields. This list is managed in Preferences-Lists. When Yate populates the list it keeps the first instance of a name and from that point on ignores variants (alphabetic case and leading article differences). The list of articles (typically 'a', 'an' and 'the') are maintained in a user configurable Natural Sort Exception set.
The action I have clears the Artist list and temporarily empties the Natural Sort Exception set. It then does a pass over a collection accumulating Artist, Album Artist and Original Artist. As there are no registered 'articles' both variants of a name (with and without a leading article) are placed into the Artist list.
I then look for all items in the Artist list which start with a leading article and remove the associated article-less variants. At this point the Artist list is 'pure'.
I then perform another pass over a collection standardizing the names in the Artist, Album Artist and Original Artist fields which results in all fields getting the names which have the leading articles.
The Batch Processor log will contain a list of every file which was modified.
This sounds complicated but it's really only a tiny action.
This way does everything unattended. You could them examine the Artist list looking for items which start with a leading article and modify it if you wish running only the second pass after making changes. This is for the rare case where you want to keep the variant without the 'The'.
The action could easily be separated into parts so you could do it in stages. ie. prepare the list and examine it, make changes then run a correcting pass. I could even produce printouts of only those relevant names.
As I said, it sounds like a lot but it is really a less manual means of doing it. Let me know what you think.