Aside from creating money that expires after so much time of inactivity, I don't know how any kind of 'money' system or systems could be created that would force (and it would have to be coercive), an initial level playing field.
I would however suggest, that both money and the vote are a means of allocating resources in an economy that uses either or both. And the vote is ( hypothetically

) a means of creating a permanent level playing field. The problem, which I suspect you are getting at, is that wealth of one form or another can be accumulated and used to bias the equation.
What we forget, and it's easy to do in good times, is that it is our responsibility to continually organize and fight against corruption and monopoly power - and that includes the government, the biggest monopoly power in our lives. Corrupt people are attracted to power like moths to a bright light and we must be eternally vigilant.
What we ought to aim for IMO, is to create something better than what we have, but it's hard to do as we have no data on what the outcome will be as there are not many experiments taking place. Therefore I support the creation of many open 'money' systems and a diverse array of systems of governance and resource allocation. The more experiments that there are the faster new systems can evolve which take advantage of accumulated knowledge.
Ultimately, there is no ultimately. . .that is to say that there can be no perfect system as we are always having to adapt and re-adapt to each other and the universe around us.