Davey:
I can't say if those factors you mention are possibilities. By 1954, major Hollywood studios were more desperate to use their capacity than anything else, because TV and the Justice Department's divorcement of studios from theatre chains had heavily damaged box-office, meaning many fewer movies were being shot than in former years. A fully-booked backlot was the stuff of dreams by then.
I don't know the shooting dates for the film (IMDb doesn't have any info, either), but it was a Christmas 1954 release, which means principal photography had to have been finished at least some months earlier. Young at Heart wasn't just a melodrama - it was a musical, and it takes a lot of post-production time to dub in the music, as well as all the other post stuff that has to be done on any movie (a later, much more elaborate, Warner's movie, 1964's My Fair Lady, took over a year in post). That makes me think it could have been shot that spring or summer. Doris's other movie that year was Lucky Me, which wrapped in February of '54, so that also suggests a spring or summer shoot for Young at Heart.
Hard to know without research. P.S.: You're absolutely right about the ending. In the original script, Sinatra's character, Barney Sloan, died after his self-inflicted "auto accident." Sinatra didn't necessarily mind dying in a movie - he'd done it before. But he didn't think it was right for this particular movie, and used his clout to get the ending rewritten. [this post was last edited: 12/19/2012-16:45]