Different LLMs hallucinate on different questions. A model that fails on obscure science may be reliable on history. We introduce CMSE, a training-free method that quantifies this cross-model disagreement. The selective cascade variant S-CMSE beats majority voting by +4.6pp on TruthfulQA while calling only 2.0 models per query on average. On contested questions where models genuinely disagree (top 15.7% by entropy), CMSE wins by +12.5pp. Uncertainty AUROC = 0.765.

HyDE degrades multi-hop retrieval by up to 7.7pp on HotPotQA. We propose CMHA, which aggregates hypotheses across N diverse LLMs, recovering the degradation and reaching R@10 = 0.8242 on NQ. We also report the first empirical evidence that chain-of-thought thinking models catastrophically break HyDE (up to 68pp degradation on HotPotQA). A diversity-based adaptive routing policy achieves 99.9% of full CMHA recall at 3.8 average LLM calls per query.

Text-to-SQL evaluations routinely co-optimize model, prompt, retrieval, and generation strategy simultaneously, making it impossible to know whether a result reflects the model or the engineering. We fix every component of ADAPT-SQL across three architecturally diverse models. The key finding: models score within 0.8pp on 89% of Spider queries regardless of parameter scale. The gap opens only on nested-complex queries, where MoE routing unlocks a +4.4pp advantage for Qwen3-235B (22B active) over Gemma4-31B (31B active, dense), an ordering inconsistent with active-parameter count alone. 91.0% execution accuracy on Spider 1.0, competitive with fine-tuned systems.