furthest words ... 'highs' (23 hops away)

path from 'about' to 'highs'
about -> abort -> aport -> sport -> spurt -> spurs -> spars -> sears -> tears -> teams -> terms -> terns -> turns -> burns -> burnt -> buret -> beret -> beget -> begot -> bigot -> bight -> sight -> sighs -> highs

furthest words ... 'signs' (23 hops away)

path from 'about' to 'signs'
about -> abort -> aport -> sport -> spurt -> spurs -> spars -> sears -> tears -> teams -> terms -> terns -> turns -> burns -> burnt -> buret -> beret -> beget -> begot -> bigot -> bight -> sight -> sighs -> signs