Okay, next wish.

In IE, I was able to make a setting change somewhere which allowed me to create a desktop shortcut to a web page, and double-clicking on that shortcut would open a new instance of IE instead of re-using the existing IE window to open the shortcut.

The option, in the Advanced properties of internet explorer, was called "Reuse windows for launching shortcuts". By unchecking this box, I got the behavior I wanted.

Now, Firefox behaves the way IE did when the box was checked. Is this a setting I can change?

Note: I am aware that I can achieve the same effect by editing the shortcut so it points to "firefox.exe <website>" instead of just pointing to "<website>" by itself. I want to have it work without the need for this edit.