As you said the crux of the issue has to do with getting every last amount of energy out of a unit of fuel. You can consider this your total fuel efficiency.
Accelerating your vehicle from rest to 60mph or 100km/h will require a fixed amount of energy based on the weight of the vehicle. (excluding wind, friction and rolling resistance).
So you need to utilize your engine in the most efficient way to produce that amount of energy. For example you could just floor the accelerator and rapidly produce the energy required but there is no way for you to know whether that path is more efficient than building that energy over a longer period of time.
To know this you need to know your engine. Specifically you need to know your Brake Specific Fuel Consumption (BSFC). The BSFC measures how much energy your engine produces per unit of fuel (usually a gram of fuel). Your engine will have different BSFC at different RPMs and Torque values. You want to run your engine where it has the lowest BSFC (lowest fuel consumption per unit of energy produced). So if you look at the BSFC chart I have linked you will see that for that engine its lowest BSFC value is 206 at about 2100-2200 RPM at close to peak torque.This means that this engine runs most efficient in that operating range.
In general engines run most efficient close to their peak torque at wide open throttle and at the lowest RPM possible. This range will be different for every engine and vehicle because all engines are different and every vehicle has different parasitic loads. You could probably calculate it for your vehicle if you run the vehicle on a dynamometer to measure the hp (energy) and then also monitor the fuel consumption and then do a division accross the curve to see where the engine was most efficient.
Now that you know at what operating conditions your vehicle is most efficient the difficulty then becomes running your engine in those conditions at all times during acceleration. This becomes difficult with a transmission because the rpms have to rise as your vehicle accelerates.
With a manual transmission what I would do with the above example curve would be to have the accelerator at wide open throttle from 1500-2500 rpm and shift at 2500rpm for each gear. I am sure that it is possible to calculate the exact shift points for maximum efficiency but I am not willing to put that much effort into it.
With an automatic transmission this is very difficult because if you try to run the engine at wide open throttle the automatic transmission will extend your shift point up to the high RPM range and you will get very bad BSFC and in turn efficiency. With an automatic transmission you have to accelerate much slower so that the transmission will shift at the appropriate points to keep your engine in an rpm where it can operate at its highest efficiency. Maybe pushing the accelerator at half throttle can achieve this but you would have to do it by feel.
In conclusion I would say the best way to accelerate is to accelerate as fast as possible in the lowest RPMs.
Hope this explanation helped somewhat.
Wiki Brake Specific Fuel Consumption