Any way to launch a separate instance of Google Chrome with a custom icon?
You could do all this via the Finder instead, along the following lines:


Within Finder, navigate to your Google Chrome app 
Select (but do not launch) the Google Chrome app 
Press commandC to copy the app
Press commandV to paste the app
Now you will have two copies of the Google Chrome browser
Select the second copy (but do not launch it)
Press commandI to get info of the app
Now navigate to wherever you have the icon you'd like to use and also Get Info (commandI) for that
In the Get Info window for the icon, select the icon at the top left and press commandC to copy the icon
Navigate back to the Get Info window for the second copy of Google Chrome (the one you opened up at Step 7)
Select the Google Chrome icon and paste (commandV) the icon you copied at Step 9
While you're at it, you may want to rename the second copy of Google Chrome


Now when you launch the two copies of Google Chrome, they will each have a separate icon.