I've been trying to find your engine, but it is one where Kawasaki has allowed JD to block the exact engine with a non published engine code AS04. Not unusual for JD. Using the JD numbers all the parts seem to have the correct part numbers, but there is no way to cross-reference them to Kawasaki. If the original heads don't fit on the short block, then you know that someone at the dealership has screwed royally in looking up parts and you should be able to return all parts which do not fit. This is not the first time I have seen JD parts (part numbers) not matching the right Kawasaki parts (part numbers). You are going to have to work this out with the people you ordered from, if they are good they will work with you, as I hope they looked up the parts you needed.