In the application of the combustion models based on low-dimensional manifolds (for instance flamelet models) to large-eddy simulation (LES) of reactive turbulent flows, the modeling simplifications of the combustion process is a critical source of uncertainty in addition to those due to the turbulent closure model and numerical discretization. The ability to quantitatively assess this uncertainty in absence of the reference result is vital to the reliable and predictive simulations of practical combustion devices. In the present study, the Pareto-efficient combustion (PEC) framework is extended to adaptive LES combustion simulations of turbulent flames. The key component of the PEC framework is the so-called manifold drift term. Its extension LES is proposed to make such assessment by examining the compliance of a particular combustion model in describing a quantity of interest with respect to the underlying flow field representation. With the focus on improving predictions of CO emissions of flamelet-based combustion models, this work employs PEC to augment the flamelet/progress variable (FPV) model through local sub-model assignment of the finite-rate chemistry (FRC) model. To this end, a series of LES-PEC calculations are performed on a piloted partially-premixed dimethyl ether flame (DME-D), using a combination of FPV and FRC models. The drift term is utilized in the PEC framework to the estimate the model related error for quantities of interest. The PEC approach is demonstrated to be capable of significantly improving the prediction of CO emissions compared with the monolithic FPV simulation. The improved accuracy is achieved by enriching the FPV model with FRC in regions where the lower-order model is determined insufficient through the evaluation of drift terms.