Speech contains both acoustic and linguistic patterns that reflect cognitive decline, and therefore models describing only one domain cannot fully capture such complexity. This study investigates how early fusion (EF) of speech and its corresponding transcription text embeddings, with attention to encoder layer depth, can improve cognitive status classification. Using a DementiaBank-derived collection of recordings (1,629 speakers; cognitively normal controls$\unicode{x2013}$CN, Mild Cognitive Impairment$\unicode{x2013}$MCI, and Alzheimer's Disease and Related Dementias$\unicode{x2013}$ADRD), we extracted frame-aligned embeddings from different internal layers of wav2vec 2.0 or Whisper combined with DistilBERT or RoBERTa. Unimodal, EF and late fusion (LF) models were trained with a transformer classifier, optimized, and then evaluated across 10 seeds. Performance consistently peaked in mid encoder layers ($\sim$8$\unicode{x2013}$10), with the single best F1 at Whisper + RoBERTa layer 9 and the best log loss at Whisper + DistilBERT layer 10. Acoustic-only models consistently outperformed text-only variants. EF boosts discrimination for genuinely acoustic embeddings, whereas LF improves probability calibration. Layer choice critically shapes clinical multimodal synergy.