I think the origin of that expression is more objectionable than only tznius.
Many operas (who frequently have “fat ladies”, women who need to have the capacity to project to a huge opera house) are not often concluded by a “fat woman” singing.
Mozart and Rossini usually have a chorus or ensemble.
Verdi and Puccini frequently have duets.
Donizetti has a variety.
The type of opera that almost always is sung by a large woman because the orchestra is so large is Wagnerian opera.
About “being over”, the length of Wagner’s operas are always excessively long, so one would ask, “When is it going to be over(finally)?”
Wagner, has a preoccupation with women, especially in “Tristan und Isolde”, where I believe this expression came from, and the final scene has the “fat lady” singing until she dies.
So I think that, definitely, frum Yidden shouldn’t use this term.
There are some cute suggestions here, but if one wants to continue in the music mode of the original, one could say “till the cymbals clash and the timpani roll.”(Just got thru listening to Mahler.) 🙂