And the hidden dates are:
20A: Relax during a drill (stand at ease). Okay, so this isn't your run-of-the-mill soldier at ease...but it came up here when I Googled the phrase. You can have your very own, if you don't mind having a couch that's butt ugly.
61A: Sunshine State school (Florida Tech). I don't know if this was a gimme for everyone. If you grew up in Florida, as I did, you know it's called the Sunshine State. Add the TE, and you don't have to be a rocket scientist to figure out the rest. Florida Tech is in Melbourne, near the Kennedy Space Center. You can read more about it here.
11D: Show sadness (shed a tear). When we cried (as kids, of course), our dad referred to them as crocodile tears. According to this article, crocodiles really do shed tears. Isn't that one of the saddest things you've ever seen?
35D: "Time to rise, sleepyhead!" (up and at 'em). This never worked in our house. We needed something like banging a metal spoon on a pan. The expression always reminds me of the cartoon superhero, Atom Ant. Here's a video of the show's introduction...it's priceless.
Only one tough spot in the puzzle. 40D: Zwei follower (drei), crossing with 49A: Trojan War hereo (Aeneas). I wasn't sure how to spell either of them. Drii and Aenias worked as well for me, but Across Lite wouldn't accept it. For those of you who don't know German (including me...thankfully, Don does), zwei is two, drei (duh) is three.
Multiword phrases make Ava a happy solver. This puzzle had several, including 24A: Polite affirmation (yes, sir), 71A: TV shout-out from the team bench (hi, mom), 4D: "Nevertheless..." (even so), 42D: Lose the spare tire (slim down), 45D: Schedule B or C, e.g. (tax form), 52D: Chooses to participate (opts in), and 54D: "Impossible!" (no way).
Liked 2D: Bring together (unite) because it reminds me of a funny t-shirt. You can order your very own here...if you're so inclined.
Didn't really know 47D: Ancient Greek colonnade (stoa), but I got it from crosses. It does, however, lead me to the Word of the Day (WOTD). Stoma: a microscopic opening in the epidermis of plants, surrounded by guard cells and serving for gaseous exchange; a mouth or mouthlike opening; esp., an ingestive opening in lower invertebrates. For those of you with weak stomachs, I'll spare you a photograph.
I'm out of time and out of words. Here's the grid...
...and I'll see you tomorrow.