There is also some confusion as to terminoligy.
The only real "0" engine is an engine that has done no hrs i.e. a factory new one.
Lycoming ( for example ) can produce a zero since factory overhauled engine but some of the components may have 2000 hrs on them e.g. the crancases.
Many refurbishers offer zero since overhaul which can be your old 3000hr crankshaft reground ( having been inspected first obviously).
You can have a "rebuilt" engine whereby it has been completly stripped and checked, all components found to be within tolerance and it has been reassembled with new seals and gaskets and returned to use.
Some LAA Inspectors are cleared on a case by case basis to split crancases on such engines.They can be overhauled in accordance with the manufacturers manual or they can be rebuilt but they cannot be called 0 timed.
That is because the LAA cannot operate on a comercial basis. It could be construed that a 0 timed engine increases an aircraft's value hence this restriction.
In reality, provided the work is done properly there is no difference, because even if you have a brand new unrun engine ,as soon as you put it in an LAA airframe it is technically " on condition".
So, just to recap, the only real "0" time engine is an unrun new engine.
Any thing else is 0 (or x) SINCE overhaul, or SINCE rebuild.