It seems like the relevant problems to solve are 1) how to provide enough support to all people so that the "floor" isn't so low as to be despairing and 2) how to help people to be mindful that sometimes, you will not be on top of the pile, and that's
OK.
Inequality itself is a function of the uncounted dimensions of comparison amongst humans. Wealth is just a proxy target for this underlying fact. Make wealth equal by the most gentle mechanisms imaginable and the dynamics will just shift to some other dimension. It's like whack-a-mole with abstract concepts we barely understand baked into our monkey brains.