Kawasaki FV420 NO START WHEN HOT
Since you have fuel & spark but it's not starting when hot, my guess would be that the coil may be breaking down once it gets hot and that the spark you're seeing is just not hot enough to ignite the fuel. If you replace the coil and it still has the problem, then it's entirely possible that the module, though new, may be defective anyway. As a side note, two other forums you might want to join that are a wealth info for small (and not so small) engine repairs are the PER small engine forum and mytractor forum.com. There are many professionals and enthusiasts on both that can help with just about any problem you might encounter on any small engine. Good luck.