Uninstall (including settings) and reinstall solved the problem. Takes only seconds to work now, once desktop is reached. Some file must've gotten corrupted.

Is there a way to change the order of items in the system startup?

Upon further experimentation, it appears to be working, but on a very long delay. IOW, about a minute after I have access to the desktop. Can that delay be adjusted?

That's the most visible feature, and the one that bothers me when it doesn't work, so that's when I open the app to make it work. So I can't answer your first question.

But as to your second question, how would your (functional) icon get into the System Tray if launch at startup is disabled? The fact that it populates the System Tray at Windows startup tells me that it's not disabled. Also, I have checked the Task Manager list, and it does show "enabled."