After shutting down the hot engine, you say it won't start. Does that mean the starter wont' turn over the engine, or it turns over (spins the engine) but never starts?
Do a spark check on each plug when it is in this "hot/no-start" condition. Do you have good spark on both plugs? If not, there's an ignition issue. If you do have good spark, it sounds like a fuel delivery problem of some kind.
If you'll share the serial number off the side of the block (GXXXX-1234567) I can share some troubleshooting steps to try.