Direct Numerical Simulations (DNS) of turbulent viscoelastic channel flows typically generate a tremendous volume of information (terabytes per run. Data reduction is therefore essential in order to allow for an efficient processing of the data, let alone its preservation for future studies. However, previous attempts, using a projection of the velocity to the top Karhunen-Loeve (K-L) modes, failed to produce velocity fields that could generate the DNS conformation field adequately. In an effort to rectify this deficiency we investigate here three different approaches that attempt to introduce small scale information. First, we extended the K-L analysis that allowed us to use a hybrid measure, based on a weight of the pseudodissipation and the fluctuating kinetic energy, as a new objective function. Second, we used a K-L decomposition of the vorticity field using the enstrophy (average of the square of vorticity fluctuations) as our new objective function. As a third attempt, we used again the standard velocity K-L approach, but in the reconstruction stage of the conformation tensor we compensated by suitably rescaling the Weissenberg number. It is shown here that, whereas the first two methods fail to give any improvement over the classical K-L approach, we were able to reconstruct fairly accurately the conformation field using the third approach, even with a relatively small set of 1714 K-L modes. The rescaling factor in that method was calculated objectively, based on the ratio of DNS vs. K-L-reconstructed based estimates of the extensional deformation rate in the buffer layer. Given that fact, we hope that this approach can also provide the starting point for future investigations into low-dimensional modeling of viscoelastic turbulence as well as other multiscale applications.