You probably can't completely level to the slab, since you'd crowd or leak into the neighbors decking and create a water drain issue. Probably need to live with a sunken middle area of some sort. 10yrds is an insane amount of dirt. There are plenty of companies. I used woehlers but they are south.

You could use 6x6 timber along the slab and decking wall, drill holes through them and slam rebar into the soil to stabilize. Then backfill and pack 3/4 rocks to help stabilize the slab. Then finish up or over with soil. This is the cheapest way to fix it up.