How I did it:
Follow the instructions here.
Just type 'Google Car Home' whenever it refers to Google Wallet.
The app will install, but then give you a message that it's not compatible. You will not see it in your apps - however if you go to settings-->apps it's in the list - there is just no icon available.
So there is a final step, install this app.
All this app does is give you a toggle to launch the default car home app. If you have more than one installed, it will as which you want to use.
I've used Google Car Home on my Verizon Nexus today and it works great. I've also changed the colors now so they match 'ICS blue'.
So there you have it! Google Car Home on your unlocked, unrooted completely stock Galaxy Nexus!
