I think I recall seeing your yard situation before. I would definitely pick your neighbors brain about how best to approach your walls. Although if I know engineers, he will be conservative and you probably wont like the cost of what he's suggesting.
Terraced walls are complicated to design because there is compounding loads transferred to the lowest wall. I think what you have in place now was more for erosion and to create planting areas rather than hold back a slope. Have you looked into cellular confinement systems?
Create Vegetated Geocell Retaining Walls that are Structurally Resilient MSE Wall Alternatives. Free Wall Design Software.
www.prestogeo.com
These can be used as slope reinforcement or as a green wall where you can plant the cells to help with erosion. Installation is finicky, but it might be a cheaper option?