  A promising route to tailoring the electronic properties of quantum materials
and devices rests on the idea of orbital engineering in multilayered oxide
heterostructures. Here we show that the interplay of interlayer charge
imbalance and ligand distortions provides a knob for tuning the sequence of
electronic levels even in intrinsically stacked oxides. We resolve in this
regard the $d$-level structure of layered Sr$_2$IrO$_4$ by electron spin
resonance. While canonical ligand-field theory predicts $g_{\parallel}$-factors
$\!<\!2$ for positive tetragonal distortions as present in Sr$_2$IrO$_4$, the
experiment indicates $g_{\parallel}\!>\!2$. This implies that the iridium $d$
levels are inverted with respect to their normal ordering. State-of-the-art
electronic-structure calculations confirm the level switching in Sr$_2$IrO$_4$,
whereas we find them in Ba$_2$IrO$_4$ to be instead normally ordered. Given the
nonpolar character of the metal-oxygen layers, our findings highlight the
tetravalent transition-metal 214 oxides as ideal platforms to explore
$d$-orbital reconstruction in the context of oxide electronics.
