Is it possible to grow anything there, save 3 or 4 bushes?

"... the former owners embedded some tire-like items in it ..." That sounds mysterious!

I don't know if this will be useful to you, but a while back I came across a method of road building that used a layer of horizontally set tires with their sidewalls removed, filled with rocks, as a sub-base for the purpose of road stabilization. It looked very effective, as well as using a material that is basically throwaway/free. The tires were rock-filled standing shallow cylinders, solidly abutting one another, and their main purpose was to contain the rocks in order to prevent them from migrating sideways. A sideways movement would eventually transfer to a disintegration of the road bed, beginning at the edges and working its way toward the center of the road over time. The tires put an end to the possibility of any sideways migration of the rocks.

This same principle could be used on a slope, but with stacked tires. The only things is, the leading edge of tire rows would show. If it could be covered by a vine or creeping growth, that would be one way to get rid of the look. I'm not sure what your possibilities for growing anything, is.

Something that lately has become rather big here are gabion walls. I don't particularly understand their use in an area where dry laid stone walls have a significant cultural history, but I can see them for your application.

@Yaardvark - I do think that's what the tire things were intended to do in this case. I'm planning to have drip irrigation lines across the slope, so I should be able to grow stuff - ideally plants that love good drainage.

@mad_gallica - Gabion walls look a bit severe, but I guess the cages could be mostly hidden by groundcover. Do you happen to know whether a drainage system would be required like with an ordinary retaining wall? Or would water just be able to flow through the rocks?

No wall drainage system needed with an innately leaky wall.