Freyd-Mitchell embedding theorem with commutative rings

Question

For a small abelian category ${\cal A}$, the Freyd-Mitchell theorem guarantees that ${\cal A}$ is equivalent to a full subcategory of ${\bf Mod}_R$ for some ring $R$ in a way that preserves exactness. The ring $R$ has unity but is noncommutative; in fact, it's of the form $\operatorname{End}(I)$ for some suitable object $I$. This theorem makes diagram chases valid for many categorical arguments, but I'd like to stay in the commutative category (e.g., for some parts of homological algebra) if at all possible. Are there any nice conditions on ${\cal A}$ that would allow $R$ above to be taken as commutative?