Update: I was able to get the stand out, but only by playing a little rougher than I'd like to with such an expensive monitor. My method was to place one palm on the back, as central as possible, and depress the latch with my thumb. With the other hand, I grasped the stand as close to the connection as I could, and did simultaneous wiggling up-and-down as well as left-and-right. It took a bit of force, and I had to go at it for maybe 10-20 seconds.

Now that I can take a look inside, it seems that the latch is indeed stuck. When I press it down, it will stay down even without me pushing it down. Even when pushed all the way down, the internal latches don't go back far enough to release the stand. When I push the internal latches instead, the outer latch will actually press even further down than I can when pressing from the outside. However, even after doing this it does not get un-stuck.

Hopefully I have been descriptive enough to help anyone else suffering from this issue.