Inverting buck-boost vs. positive buck-boost
The appnote you are citing sounds as if it uses slightly different terms to describe the same working conditions for both inverting and positive buck-boost topologies.

A classic buck-boost (simple flyback toplogy) that uses a single winding inductor always inverts its voltage. To make it non-inverting, a second take-off winding is typically added, which can be wired the other way around to make the voltage come out the same as the input. With a two winding buck-boost (flyback) you can also completely isolate the secondary. You can also change the turns ratio to optimize for different input/output voltage ratios.

In your case, if you only want to drive LEDs, and they don't have to be referenced to GND in any particular way, there's no reason you can't use an inverting buck-boost, which, by only requiring a single-winding inductor, might be simpler.

However, as another answerer has pointed out, the ranges you give for your input and output voltages are quite wide. Without knowing more about the predominant operating conditions, it's impossible to give advice to help optimize efficiency.