I'd be very interested to find out more as I always understood that there is no path to GC from E3. Others have also suggested that entering the GC lottery could jeopardize E3 renewal as it demonstrates an intent to become a permanent resident.
I am also on an E-3 visa, but as far as I understand there is no path to obtaining a green card. The intention of the E-3 is that you will not remain permanently in the US and so it is not possible to become a permanent resident.
I wonder how many tech executives don't use email?
I've got a feeling Tim Cook doesn't use a computer, maybe just an iPad with a carefully curated list of messages and financial reports for him to browse.
In my experience I have found it more difficult to work less days and take holidays as a contractor. The company that is paying for your services expects complete short term dedication on delivering the project, and that is what you should provide. You can take longer breaks between contracts but again I have found that not to be the case as you always want to have more work lined up for a steady income stream.