The suggestion to get a landscape architect in might work but it's just as likely that they won't come out for a small job. You can find out more yourself and this will guide your decision:
- what is the soil? does it retain water (organic based) or does it shed water (clay)
- can you buy more of the native vegetation which is growing there already?
- do you have neighbours that you can ask what they have done?
- does your area have any history of landslides under unusual amounts of rain?
- when it rains where does the water go?
This last is the most important. If local low spot is the area shown in the picture then a complete solution is to use some combination of french drains and dry wells with four inch diameter corrugated plastic pipe with sleeve. No solution that only deals with the slope will be satisfactory if the low area is under water after a good rain.
The link you posted to a honeycomb grid which you put in the soil might work if you combine it with native plants that have a good root system and have somewhere for the water to go at the base of the slope.