Cross-Domain Sequential Recommendation (CDSR) seeks to improve user preference modeling by transferring knowledge from multiple domains. Despite the progress made in CDSR, most existing methods rely on overlapping users or items to establish cross-domain correlations-a requirement that rarely holds in real-world settings. The advent of large language models (LLM) and model-merging techniques appears to overcome this limitation by unifying multi-domain data without explicit overlaps. Yet, our empirical study shows that naively training an LLM on combined domains-or simply merging several domain-specific LLMs-often degrades performance relative to a model trained solely on the target domain. To address these challenges, we first experimentally investigate the cause of suboptimal performance in LLM-based cross-domain recommendation and model merging. Building on these insights, we introduce WeaveRec, which cross-trains multiple LoRA modules with source and target domain data in a weaving fashion, and fuses them via model merging. WeaveRec can be extended to multi-source domain scenarios and notably does not introduce additional inference-time cost in terms of latency or memory. Furthermore, we provide a theoretical guarantee that WeaveRec can reduce the upper bound of the expected error in the target domain. Extensive experiments on single-source, multi-source, and cross-platform cross-domain recommendation scenarios validate that WeaveRec effectively mitigates performance degradation and consistently outperforms baseline approaches in real-world recommendation tasks.