Serving Large Language Models (LLMs) often requires choosing between stronger reasoning and lower inference cost. Model merging offers a practical way to build several models between a reasoning-oriented model and a cheaper base model, but common model-level merging methods usually control this trade-off with only one or two global knobs. We study this setting as a multi-objective optimization problem: instead of producing one merged model, the goal is to find a set of merged models that cover different accuracy--token-cost preferences. Layer-wise merging is more flexible because it can assign different merge weights to different Transformer layers. However, it introduces two practical challenges. First, the layer-wise search space is large, and existing methods often search it without using helpful signals from the source models. Second, LLM evaluations can take very different amounts of time, so synchronous batch optimization wastes GPU time while waiting for slow evaluations. We propose Asynchronous Prior-Guided Bayesian Model Merging (AP-BMM). AP-BMM uses parameter and reasoning-activation differences between the source models to suggest which layers should matter early in the search. It also uses an asynchronous Bayesian optimization loop that accounts for candidate models already being evaluated. A lightweight reranking step further spreads candidates across the accuracy--cost trade-off. Under fixed evaluation budgets, AP-BMM achieves stronger Pareto-set quality and broader trade-off coverage than synchronous layer-wise baselines and representative model-level merging baselines. Compared with the synchronous Bayesian baseline, it also reduces wall-clock time by improving GPU utilization. Code: https://github.com/MiLab-HITSZ/AP-BMM.