About sixty years ago our parish in Jersey City had curate who taught scripture at a university level.  His sermons were frequently very dry, but loaded with scholarship and insight.  When this gospel was read, he also explained the custom of the time, exactly as you mentioned.   Unfortunately few of us understood the importance of his erudition, and let it pass into forgetfulness.  Luckily for me my grandmother was one of the few.  Thanks to her I've been able to share his exegesis whenever this gospel comes around.  Surprisingly I have never again heard this interpretation, even from prominent scholars.

Thank you for confirming his words.  It's been a long time.

God be with you