We ask whether a low-weight data2vec-style Exponential Moving Average (EMA) self-distillation auxiliary (𝜆=0.1, 𝜏=0.999) improves a small masked language model at the BabyLM-2026 Strict-Small scale. Our base model is a 33M-parameter LTG-BERT encoder with GPT-BERT-style hybrid masked/causal training, trained from scratch on the official 10M-word corpus in 2.3 GPU-hours on a single NVIDIA L40S. A substantial gain in Entity-Tracking during early development from adding the auxiliary motivated the study, but disappeared in later re-evaluation. In a comparison across 6 seeds, no evaluation task changed significantly (aggregate effect p=0.29), and the early gain is best explained by seed noise. Several variants intended to strengthen the auxiliary do no better. We attribute the model’s competitive scores to its hybrid training recipe and to EMA weight-averaging, both already established.