After I run my 08 Fit for an errand or two and shut it off, I have to wait an hour or so before it will restart. It turns over fine just will not start. I suspect it to be a fuel delivery issue...? Has anyone had to solve this mystery?

 

I don't think it's a fuel delivery problem if the car will start once cold. I'm thinking it's a fault with a temperature sensor or sensors with the engine coolant. The car reads the current temp to adjust what sort of fuel mixture to run at. If the voltage is out of spec the car assumes a sort-of worst case scenario and will start rich. If the engine is already hot it'll not start. To prove this you either need to be pretty proficient with a voltage meter and/or the means to talk to the car's computer. Here is where to start looking. this is more powerful than the ordinary OBD 2 bluetooth reader. You're looking for a voltage when hot of .5 to .7 on one or both of your temperature sending units.

 

Your symptoms sounded like vapor lock on a carbureted car... LOL.

I had a similar issue on a fuel injected Nissan years ago. Car either does not start after running for a while and turning off the engine (heat soak) or would stall shortly afterwards.
Turns out that it was the coolant temp sensor going bad.

I would start with Red 05's advice.