  We provide polynomial lower bounds for residual finiteness of residually
finite, finitely generated solvable groups that admit infinite order elements
in the Fitting subgroup of strict distortion at least exponential. For this
class of solvable groups which include polycyclic groups with a nontrivial
exponential radical and the metabelian Baumslag-Solitar groups, we improve the
lower bounds found in the literature. Additionally, for the class of residually
finite, finitely generated solvable groups of infinite Pr\"{u}fer rank that
satisfy the conditions of our theorem, we provide the first nontrivial lower
bounds.
