LED determining Series / Parellel configurations for most efficent design
LEDs are current driven devices, not voltage driven. Hence, as long as the drive current requirements are met, the voltage involved is merely a dependent variable, so to speak.

For both types of LEDs mentioned, a constant current buck LED driver would probably provide the lowest cost Bill of Materials for a very high efficiency design. 

For instance, the Texas Instruments LM3407 constant current, floating buck converter will allow a supply of 4.5 to 30 Volts, and a LED string forward voltage of anywhere between 10% and 90% of the supply. Taking the voltage numbers provided in the question:


Vin(min) = 11.8 Volts ==> maximum Vf of string = 0.9 x 11.8 = 10.62 V
Vin(max) = 28 Volts ==> minimum Vf at full input voltage = 0.1 x 28 = 2.8 V


So, as long as each string is between 2.8 and 10.62 Volts Vf, this regulator can support the application. Typical implementation, taken from the datasheet: 





By using switching current regulators, the issue of getting rid of surplus voltage as heat is pretty much eliminated. As can be seen from the example of the LM3407 above, switching regulators aren't too fussed even if 90% of the supply voltage needs to be dropped within the regulator: The device does cycle-by-cycle current regulation of the load (the LEDs), and simply switches off the rest of the time, hence not needing to dissipate the excess voltage as heat. 

This simplifies the series / parallel LED decision significantly: Simply put as many LEDs in series as you like, up to the maximum determined by the supply voltage lower limit (10.62 Volts as calculated above). 

Thus, 3 LEDs of 3.4 Vf, or 5 LEDs of 2.2 Vf can be supported per string, in this particular application.