I had forgotten but it turns out I already am using the Tag Panel in my attempt to capture the Grouping tag. I define it with field CONTENTGROUP which is the field/tag MC uses. But here's what's weird:
When MP3tag is used to insert non-blank CONTENTGROUP, it gets read/displayed by MC as blank.
When MC is used to insert non-blank CONTENTGROUP, it is read/displayed by MP3tag correctly as non-blank.
I don't know what to conclude it, whether the issue is with MC or MP3tag!
LATER: I've now resolved the issue! I used Tag Panel as you suggested but rather than select CONTENTGROUP, one of the available tags, I simply manually entered the name GROUPING - which was not one of the tags listed - just to see what it would do. And it turns out that works!
Thank you kindly for your help!