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How do I deal with collision resolution causing another collision?
It sounds like you want to simplify collisions instead of using actual inertia and other physical forces. If that's the case, could you not just make any person who is 'knocked over' become a passive object as far as collisions go? i.e. they start getting smooshed and so can't be smooshing others.
Is it better to hard code data or find an algorithm?
Just to clarify your confusion, I think the OP when referring to a 5x5x5x5x5x5 hex grid was not referring to 6 physical (or virtual) dimensions, but instead a hexagon of hexagons, where each side of the hexagon contains 5 smaller hexagons along its length, similar to this (ignore the black dots). In that case the board would contain 9+2(5+6+7+8) cells.