Cover is a re-interpretation engine, not a copy machine. Left alone it 'improves' your melody into something else. Faithfulness has to be demanded.
1. Say 'same melody' three ways:
faithful cover, same melody and phrasing, do not change the tune
One instruction gets ignored; three stacked instructions get obeyed.
2. Keep style-influence/variety LOW. High settings are literally 'be creative with this.' For faithful covers you want the minimum.
3. Change ONE thing. If you're covering to fix the voice, change only the voice description. Every additional change (new instruments, new genre words) is permission to drift further.
4. Cover in short sections if the full song drifts — cover the verse alone, the chorus alone. Short covers stay tighter to the source.
5. The nuclear faithful option: stems. Get Stems of the original, keep everything, and only re-render the part you want changed (new vocal via vocal-only cover), then mix it back. Total fidelity, zero drift.
Good luck! Hank founder of SonorixPG