"We will have to find some sort of tax system that makes it possible for those who can't participate in the elite to also live their lives"
Rather than a tax system that gives them pretty much no incentive to get a job (if you were essentially paid to do whatever you wanted to do, would you want to get a job?), it would probably be better to have government enforced jobs (IE: you want money from the government, you need to work for them until you find a regular job. Otherwise, you get nothing).
As I've said before, Norway has a de facto system that works like this already. Anyone that's deemed unfit to get a well-paying job gets a fixed monthly payment from the government.
What if you want more money than you can get through this system? Then you have to do work that pays. Money and status works relative to your peers, so there's an incentive to earn more if your peers are richer than you. I don't see that this is a problem if the society is wealthy enough.
You're line of reasoning is way off base. You're trying to shoehorn a scarcity-based economy into a post-scarcity society. The idea of "contributing" (the way its currently thought of) will have to go away completely. Private ownership is a social construct. In a post-scarcity world our ideas of private ownership will have to change. Society will simply not allow the owner of Acme robot company to literally own everything (because he has a monopoly on labor). A more communal-based society will necessarily spring up. No one will stand for a monstrously imbalanced society.
you want money from the government, you need to work for them until you find a regular job
So you're saying the government should hire all the unemployed? That sounds like a surefire way to make even more people unemployed in sectors that have to compete with the government's army of cheap laborers.
Rather than a tax system that gives them pretty much no incentive to get a job (if you were essentially paid to do whatever you wanted to do, would you want to get a job?), it would probably be better to have government enforced jobs (IE: you want money from the government, you need to work for them until you find a regular job. Otherwise, you get nothing).