Oh, I loved this puzzle! Loved the theme, loved the theme answers, loved much of the nontheme fill.
The theme answers:
16A: Ad icon since 1914 (Morton Salt Girl). When it rains, it pours. Do their ads still say that? Here's the original...way before my time.
37A: Oswald Cobblepot's nom de crime (Penguin)...played by Burgess Meredith in the Batman TV series. I didn't see any of the Batman movies...was the Penguin character still around?
11D: Caretaker for the Banks household (Mary Poppins).
24D: Churchill predecessor (Chamberlain). Why didn't I know that? Fortunately, I had enough of the crosses to guess the rest.
And it's all wrapped up at 56A: What 16- and 37-Across and 11- and 24-Down were all known to do (carry umbrellas).
I was sure I had something wrong when 56A was ending in LAS. Pleasant surprise.
Some excellent nontheme answers, among them:
9A: Poor box contents (alms).
19A: Acupressure technique (Shiatsu).
20A: Tree sacred to Druids (yew). I had oak at first...but 21D: Itty-bitty (wee) confirmed the error of that answer.
22A: Regular at Kelsey's Bar, on TV (Archie). Bunker, I guess. I remember that he hung out at some bar.
28A: Rebel yell (wahoo). Also the name of a restaurant that makes really good fish tacos.
34A: It could easily go up (fire trap). There was a horrifying accident outside our office today...a cement truck carrying a full load took a sharp curve way too fast and skidded, landing on the driver's side with a sickening sound. Gas was leaking and the driver was trapped. It all turned out okay, thankfully. He had only minor injuries, and the truck didn't blow. We watched two cranes work for an hour to set the truck upright...that part was fascinating.
44A: "The Female Eunuch" author (Greer). Is this something I should add to my list of books to read?
48A: Recipient of a 1937 wooden Oscar (Bergen).
52A: Impatient (anxious). A great word...an X and three vowels in a row. I don't recall ever seeing it in a puzzle.
67A: First batter to hit a home run against every Major League Baseball team (Sosa). Good guess on my part.
5D: Musical with the song "Easy Street" (Annie). Didn't remember NYC the other day...don't remember this one.
6D: Arno city (Pisa).
7D: Ignore the lyrics? (scat). I've never heard it used to mean that. I always think of the biological definition. Scat = animal droppings.
29D: Bottled spirit (Jinni). Have never seen this word and thought it was probably wrong.
30D: Element whose name roughly means "lazy" (argon).
43D: Dishevels (tousles). I like the clue and the answer.
44D: Literary monogram (GBS)...a nice change from TSE.
Favorite clues include 29A: One may hold the mayo (jar), 32A: Mend (atone), 38A: Boxer's hand (paw), 41A: Prig (bluenose), 63A: Roast setting (dais), 1D: Half a huge cost? (arm), with the same clue at 42D (leg), 4D: Place to pick up a puppy (pet shop) and 54D: Opening day? (Xmas).
And two very cool rhyming words...13A: Pleasure seeker (roue) and 47D: Grimace (moue).
That's it for today. Here's the grid... [which contains an error. 9D: is ARG, making 15A reap. Thanks to annielee for catching that.]
...and I'll see you tomorrow.