Okay, I'm replying to my own previous post here.
First of all, thank you for all the cred and XP, everyone! My email account didn't know what to make of the sudden influx of notifications from the same source and marked them all as spam. You made AOL Mail (Yes, I'm posting from 1995) go: "Hmm...who's this EA? Electronic Arts? One of the biggest publishers of video games in the world? Nah, can't be. Spam it."
But really, though, all credit really goes to Reddit user: Subtractive_. Thank you, Subtractive_! Your post on Reddit got my game working again.
Secondly, as I said already, I finally got Andromeda working again!
I followed both suggestions I found in Subtractive_'s Reddit post. These were, again:
a.) Rename the 'Saves' folder within the Mass Effect Andromeda directory in 'My Documents' to anything else (in my case, 'Baloney,' because it was literally the first word to come to mind -- I don't know what that says about me) and repair the game by right clicking on Andromeda in your Origin game library menu and select 'Repair Game.'
and/or
b.) Delete BOTH the Andromeda .exe and the Sample/Demo .exe in the game's root menu (where everything is installed) and then repair the game using the same method as above.
Whether you try one, the other, or both, Origin will rewrite your saves and missing files depending on what you deleted when it repairs the game, so don't worry about losing progress as long as you have cloud syncing enabled. After that, you can delete your old, renamed save folder.
I did both of these and got Andromeda working again! I don't know which one did the trick, but clearly one of them did so.
Here's the caveat (there's always one, isn't there...?):
I CANNOT launch Mass Effect Andromeda from a shortcut anymore. Period. I can only launch Andromeda from within Origin. Then, it works. But if I try to launch it from a shortcut, it just takes me to the game's menu in Origin. And then, from there, I can launch the game. Is it inconvenient? Somewhat. Is it game breaking? Heck no.
So, if you're trying to launch Mass Effect Andromeda from a shortcut after trying Subtractive_'s suggestions, and they still don't seem to work, then try launching from within Origin itself. If that still doesn't work...well, then, sadly, I don't know what to tell you.
If you're still having problems launching Andromeda, make sure you contact EA/Origin tech support to get one-on-one help and also make a bug report on the Origin website to inform the devs (you don't get a reply from bug reports, but it informs the devs of the circumstances around your bug). The more tech support and the devs themselves hear about this and other bugs, the more likely it is they will be able to squash them.
Thanks again for the XP, everyone, and I hope I've helped, if even a little. Have an outstanding day!