Your question boils down (ha!) to whether gasoline  vapor would be
better to use as a fuel than a gasoline aerosol, where better means
to release the greatest amount of net energy. Existing
engines leave some fuel unburned and consume some energy in
heating the liquid to the point of ignition.  Your proposal to preheat
and vaporise the gasoline makes sense only if it consumes less energy
than it returns in greater efficiency.  It also needs to be practical:
for
example, you alluded to the need to prevent early ignition of hot
gasoline
vapor (variously called "knocking" or "explosive destruction of
vehicle"
depending on severity).

To take it to the next level, determine the efficiency of existing
engines
and the proposed efficiency.  Use the correct units: J/Kg would be
incorrect.
Use MPG to attract investors.
-- S

Suppose that our fuel tank was very safe, and 100% safe from
explosions.

Instead of fuel injectors, why not heat up the fuel, and pump this
high pressure gaseous vapor into the pistons?

Currently, liquid gasoline is sprayed into the pistons.  From what I
understand, the finer the mist, the better and more thorough the
combustion.

Since the gaseous gasoline is the limit to how finely you can atomize
the gas, I would think that this is the most optimum way to put gas
into the cylinders.