Encourage fungi to live in the soil. Oyster mushrooms have a good track record of digesting petroleum.
Do any of your neighbors go mushroom hunting? You might go with them when they look for oyster mushrooms, and take a little rhizomorph (from just under the surface) to propagate into a woodchip mulch over the surface of your spill.
Scott Kellogg & Stacy Pettigrew wrote an interesting
book on ecological/economic restoration. The method from that book is as follows:
1. Soak cardboard in non-chlorinated water for a few minutes
2. Tear the cardboard open to expose the corrugated curls. Place the rhizomorph on the open face of one piece of cardboard, and cover it with a second one.
3. Rewet, being careful not to damage or wash away the rhizomorph, and place the cardboard in a shady location. Keep damp.
4. Check once a week to see if the mycelia have colonized the cardboard.
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After the mycelia have thoroughly colonized the cardboard, they can be mixed with more cardboard...Alternatively, a piece of colonized cardboard can be mixed with a bucket of coffee grounds
And from there, you have spawn that can be mixed in with woodchips (maybe with some straw) and kept moist until mushrooms appear on top of the spill. Apparently, the mushrooms are not reliably safe to eat, but they should allow the lawn to return. You might need to bring the nitrogen level of that soil back up, perhaps by seeding the fungus-filled spot with clover.
Mushroom spawn is also available commercially, if you want to go about it a little quicker.
"the qualities of these bacteria, like the heat of the sun, electricity, or the qualities of metals, are part of the storehouse of knowledge of all men. They are manifestations of the laws of nature, free to all men and reserved exclusively to none." SCOTUS, Funk Bros. Seed Co. v. Kale Inoculant Co.