Answered my own question after a little more searching and experimentation. Figures I'd spend three hours looking for this, ask about it here, then find it immediately after.
You need to make sure the "Align art to pixel grid on creation and transformation" button is "unchecked" (unchecked in my version of CC means 'not surrounded in a darker shade of gray').
The worst part about this button is that there is no specific window where you can find it. It's not in transformation, pathfinder, or any other window that might make sense.
This button is in the top-right corner of the main Illustrator window. underneath the "Search Adobe Stock" search bar. See picture:
It's the button that looks like 3 little blocks and a magnet.
If the button is not there, which it wasn't for me, you need to reset your panel layout.
Method 1 (the one I used):
Click on the panel layout button, again top-right of the main Illustrator window, and click "Essentials". Please note that depending on your current panel layout this button will say the name of your layout with a dropdown ("Essentials" by default, I think) or it will be an icon. If the button is still not there, go back to the same button and click "Reset Essentials".
Method 2 (untested, please confirm!):
Click in menu: Window > Workspace > Essentials
If the "Align art to pixel grid on creation and transformation" button is still not there, click the panel layout button, now in the top-right corner (labeled "Essentials" with a dropdown) and then click "Reset Essentials".
On a side note, I find this is extremely annoying since I liked my custom layout.
Hope this helps someone out there.