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Software migrations are frequent and high-stakes industrial activities. Although large language models (LLMs) are increasingly used in software development, their suitability for migration remains uncertain because migration requires semantic preservation, project-specific context, security, and production accountability. We investigate why practitioners undertake software migrations, what motivates and constrains the use of LLMs for migration, where LLM assistance is considered acceptable, and which factors determine trust in LLM-migrated code. We conducted a practitioner survey with 61 retained industry respondents, combining an internal industrial sample with an open professional survey. We analyzed closed and Likert-style items quantitatively and interpreted open-ended responses thematically. Migration was primarily framed as a bundled quality-risk activity: maintainability, scalability, and security were the dominant motives, while cost reduction rarely appeared as a standalone driver. Respondents valued LLMs mainly as accelerators for exploration, prototyping, and routine transformation, but not as autonomous migration agents. Acceptability was strongly bound by scope and control: 62.3% considered LLMs acceptable most of the time or almost always for single-file migration, compared with only 4.9% for entire-project migration. Trust depended chiefly on semantic correctness, project-context awareness, security, verification evidence, and provenance disclosure. Practitioners do not reject LLM-assisted migration outright; rather, they adopt a conditional trust model. LLMs are viewed as useful migration accelerators, but acceptable production use depends on bounded scope, human review, assurance evidence, traceability, and clear accountability.