Many of the recycled "faux," slate is made with tires, (and almost as expensive.) I have experiment a little but the labor to cut them up outdoes their use. I have tried to think of other ways, but without big machines and many tires, it just doesn't work. Now, many places don't ever through their tires out, which is a good thing, they recycle.
I have seen carpet roofs as well and done a few. I like the felt carpet padding more than the carpet. I would use it with the pitches I mention above and the same coverage or better. I can't recommend the concrete as I don't care for the stuff. It is not environmentally sustainable to keep making it in most areas. It hangs onto moisture too much and the carpet would probably have been fine with out it or just a good lime wash. I'm glad Alder had success, I just don't recommend the stuff to often, especially for green or natural builds.
It did add rigidity to the roof, so if I were to plan to do without it altogether I would have beefed up the frame and deck underneath....in the case of the cabins in question, this was bamboo and pine poles and then two thicknesses of heavy two-ply furniture crate cardboard.
It sounds like your application of concrete was a recycle/salvage and I can see that being wise/resourceful. As for "beefing up," the frame and deck, I don't believe you would have needed to if it has lasted this long. Concrete did not add any "water proof," qualities to the roof, only weight. Your roof would have been lighter without it, but it would seem your cabin has fared well, none the less. Concrete stucco, and similar applications are often added as water proofing methods, that in all actuality, only retain water and make things heavier and/or promote decomposition of the substrate through retained moisture and alkalinity. Your concept of carpet was great and has probably been the largest promoter of having things grow on the roof. I would alter my other entry, by saying, if you design a stout frame and applied the correct waterproofing, a carpet roof would probably turn green rapidly for held vegetation and compost material. The carpet padding I use is covered in moss in no time. Concrete in general is often endowed with qualities it doesn't really have, I blame the industry for that as well as many contractors that use it for their convenience, not because it is best practice. Most stick frame construction sitting on concrete foundations is not meant to, nor will it last, as long as the old timber frames, and earth structures they have tried to replace, folks like you and sites like this are beginning to open peoples eye's.