What should I do about soil contaminated with foam rubber?

I moved into a house with a very small yard this past winter. When the snow receded, I found that apparently someone had dumped some rubbish in the back yard at some point. Most it had been removed, but there were still chunks of foam rubber, shredded fabric, broken toys, bits of plastic and glass, nails, etc. I think the foam and fabric probably came from an old couch.

I gathered up the bigger pieces and thought I could rake up the rest, but no matter how much I raked, tiny bits of foam and plastic kept turning up in the dirt.

I concluded that I would simply have to remove several cm of soil altogether (I considered sifting it but decided it wasn’t worth the effort). So I’ve started scraping up the dirt and putting it in the bin with household garbage. I’ll have to spread it out over many trash days because if I just fill the trash bin with dirt it will be too heavy.

Is a better way to deal with this? I’d like to plant a garden back there, but I’m afraid to grow food in soil that has this stuff in it.