  Previously, it was shown that a superconducting state dominated by singlet
$d_{x^2-y^2}$ intra-band pairs emerges from the fluctuation exchange
approximation (FLEX) applied to a realistic model for Sr$_2$RuO$_4$, a result
that is increasingly in alignment with experimental data. Here we apply FLEX to
model the strain-dependent phase diagram of Sr$_2$RuO$_4$ and show that we are
able to reproduce its unusual features. This adds weight to the argument that a
predominantly $d_{x^2-y^2}$ singlet pairing state represents a reasonable
starting point for describing the superconducting properties of Sr$_2$RuO$_4$.
