Applying deep learning methods to electroencephalograph (EEG) data for cognitive state assessment has yielded improvements over previous modeling methods. However, research focused on cross-participant cognitive workload modeling using these techniques is underrepresented. We study the problem of cross-participant state estimation in a non-stimulus-locked task environment, where a trained model is used to make workload estimates on a new participant who is not represented in the training set. Using experimental data from the Multi-Attribute Task Battery (MATB) environment, a variety of deep neural network models are evaluated in the trade-space of computational efficiency, model accuracy, variance and temporal specificity yielding three important contributions: (1) The performance of ensembles of individually-trained models is statistically indistinguishable from group-trained methods at most sequence lengths. These ensembles can be trained for a fraction of the computational cost compared to group-trained methods and enable simpler model updates. (2) While increasing temporal sequence length improves mean accuracy, it is not sufficient to overcome distributional dissimilarities between individuals’ EEG data, as it results in statistically significant increases in cross-participant variance. (3) Compared to all other networks evaluated, a novel convolutional-recurrent model using multi-path subnetworks and bi-directional, residual recurrent layers resulted in statistically significant increases in predictive accuracy and decreases in cross-participant variance.