I don't think there is any way to set the Grouping field to respect the 'ignore words' setting. The only fields that do this are Title, Album, Artist, Album Artist and Composer.
If you don't use, and won't use in the future, the Composer field, you could probably use this to do what you want here (instead of using the Grouping field).
I think your only other option is to set the Grouping field to be how you would like it sorted (i.e. 'Beatles' instead of 'The Beatles') and you have already dabbled with this idea.
You could post a wishlist request but this seems something of a niche use case - at least it does to me, but then you never know....