We develop a modified power-counting within the heavy quark effective theory (HQET),
that results in a highly constrained set of second-order power corrections in the heavy quark expansion, compared to the standard approach. We implement this modified expansion to determine all $\bar{B} \to D^{(*)}$form factors, both within and beyond the Standard Model, to $\mathcal{O}(\alpha_s, \alpha_s/m_{c,b}, 1/m_{c,b}^2)$. Using measured $\bar{B} \to D^{(*)}\ell \bar{\nu}$ differential branching fractions for light leptons ($\ell = e, \mu$), we constrain not only leading and subleading Isgur-Wise functions, but also the $1/m_{c,b}^2$ corrections from subsubleading terms. We provide updated precision predictions for $\bar{B} \to D^{(*)}\tau \bar{\nu}$ decay rates, lepton universality ratios, and the CKM matrix element $|V_{cb}|$.