You already had half of the solution: create a variant of the page you want to differ and apply audiences to it (audiences work the same as user criteria and can even reference them). Put the order for the variants in the correct way, so you have the variant with the 'lowest' role last, since users with 'higher' roles, probably also have the 'lower' ones.
Please mark any helpful or correct solutions as such. That helps others find their solutions.
Mark
