Okay, so I guess I figured this out.
I was running AdobePatchInstaller.exe --mode=silent
straight from cmd.exe
. When I would do this, I would receive a window with progress and a final "OK" button, as I mentioned above.
However, when I ran start /wait AdobePatchInstaller.exe --mode=silent
from the command line, much like I would in a batch file, the patch seemed to install silently without fail.
Not sure I understand the difference, but it worked fine just the same.