Well, here is what I've learned.
In a new user, Photoshop saved the file instantaneously. However, this was a file I had opened off of the desktop, and not from Lightroom as I normally do in my user account.
So I went back into my user account, and opened the same file from the desktop. What do you know, it saved instantaneously! Hmmm...
Next, I went back into the new user account, imported the image into LR, and used the "Open in External Editor" command to open it in Photoshop. I made a few changes, flattened, and saved the file. Again, it saved instantaneously.
So I have isolated the problem to be with any files I open from Lightroom into Photoshop using the "Open in external editor" command. When I save those files in my account, it doesn't happen instantaneously like in all other situations described above. Instead, I get a "writing TIF format" progress bar for about 10-15 seconds. The kind of progress bar I'd expect if I was saving a 150 MB file with 20 layers.
But even though the problem is more isolated, I don't have a clue how to fix it. Any ideas?