The systems mentioned ( Mac and Windows ), they are positioned in the most interactive or important location. So in these terms, Ubuntu has it right - but I take the point about the logo and applications not being synonymous.
1) Don't have the logo highlighted with the Applications text when the menu is displayed. This would disassociate the logo, but look a bit disjointed and over-involved in my opinion.
2) As suggested, make the logo the System menu. I prefer having the system menu labelled however. The first thing I say when showing someone Gnome is how the "Start" button has lots of different functions pureed into one crowded area, but here it's thought out a bit better. It gives them a lot of confidence in the system and they usually react by saying how the never realized how confused they were by the windows menu until they saw it done better (go Gnome!!)
3) Replace the power button on the right with the brand. Not exactly a proud place to put your brand - on the back-door mat.
4) I like the number four, but I can't think of and idea to put here.