I appreciate all of your effort in trying to update and resolve this yourself. Since you're still unable to, allow me to step in and lend you a hand in updating your QuickBooks and ensure that you'll be able to open it.
This sort of behavior is often the result of QuickBooks functionalities being blocked from getting the update. To get past this, I recommend that we go to our Downloads and updates page and directly download the latest release patch from there. The steps below will guide you through the process:
Thanks for the info. It is not quite correct, however. The "Downloads and updates" page indeed downloads the older version that the original poster indicated, 188.8.131.528 R05.
In order to download the correct and most up to date version of QB 2016 for Mac Currently 184.108.40.2066 R33), you must click on the green "Download" button, and not on the "Already Downloaded? Get the latest updates" link below it. It just looks like someone didn't update that link with the current information for quite some time.