I don't think Lyco are the only firm which can zero time an engine in any meaningful sense.
If "any meaningful sense" means a legal zero-time, then yes. The manufacturer is the only one.
Regarding "zero timing" the engine, if it has had a major overhaul does this not "zero time" the engine to all intents and purposes (regulatory / performance)?
No, it does not.
Overhaul means to inspect and find within tolerances. A common misunderstanding is the belief that overhaul means to make like new or refurbish. The fact is that an engine inspected and found within tolerances is considered overhauled, and engines are often sold as "overhauled" when many of the same used parts are put back into the engine. Be careful when making assumptions about what's been done to the engine based on an "overhaul," or confusing terms such as "zero-time," "rebuilt," and "overhaul." These have very different meanings that don't interchange.