The elastic Cosserat micropolar continuum theory introduces independent rotational degrees of freedom~$\bar{\boldsymbol{\theta}}$ alongside the displacement field $\boldsymbol{\varphi}$. These micro-rotations are described by a rotation tensor field $\bar{\boldsymbol{R}}(\bar{\boldsymbol{\theta}})\in\mathrm{SO}(3)$. Their interaction with the macro-rotation field, described by the rotational part of the deformation gradient $\boldsymbol{F}$, is governed by the Cosserat couple modulus $\mu_{\mathrm{c}}$ via the Cosserat strain $\bar{\boldsymbol{R}}^{\mathsf{T}}\boldsymbol{F}-\boldsymbol{I}$. For large values of $\mu_{\mathrm{c}}$, the two rotations coincide. In this work, we examine a structural compatibility issue that arises in finite element discretizations of finite-strain Cosserat micropolar continua for large $\mu_{\mathrm{c}}$. When using a formulation purely based on Lagrange elements for both the displacement and micro-rotation fields, the structural mismatch between the classical discretizations of $\boldsymbol{F}_h=\mathrm{D}\boldsymbol{\varphi}_h$ and $\bar{\boldsymbol{R}}_h$ can lead to locking phenomena. We introduce a novel, geometric, structure-preserving interpolation framework that employs a more suitable function space for $\bar{\boldsymbol{R}}_h$ and allows closer alignment between the micro-rotation and the polar part of the deformation gradient. This construction places the relevant quantities in spaces of comparable structure. We outline the formulation, explore suitable discrete pairings, and present numerical benchmarks showing a significant reduction in locking, demonstrating the potential of this approach to mitigate locking in Cosserat finite element models.