Pseudo-labeling (PL), a semi-supervised learning (SSL) method where a seed model performs self-training using pseudo-labels generated from untranscribed speech, has been shown to enhance the performance of end-to-end automatic speech recognition (ASR). Our prior work proposed momentum pseudo-labeling (MPL), which performs PL-based SSL via an interaction between online and offline models, inspired by the mean teacher framework. MPL achieves remarkable results on various semi-supervised settings, showing robustness to variations in the amount of data and domain mismatch severity. However, there is further room for improving the seed model used to initialize the MPL training, as it is in general critical for a PL-based method to start training from high-quality pseudo-labels. To this end, we propose to enhance MPL by (1) introducing the Conformer architecture to boost the overall recognition accuracy and (2) exploiting iterative pseudo-labeling with a language model to improve the seed model before applying MPL. The experimental results demonstrate that the proposed approaches effectively improve MPL performance, outperforming other PL-based methods. We also present in-depth investigations to make our improvements effective, e.g., with regard to batch normalization typically used in Conformer and LM quality.