Welcome to Permies, Em.
You'll never get it all if it's been there for any time. I suggest either get comfortable with a less-than-perfect state of organic in that bed until it works itself out, or dedicate the bed to something that will be of benefit in the space that isn't edible.
If you're at all like me, and happen to have limited optimal garden space, you've just toxified your single best option with regards to sun or water or some other damn thing. If you can't deal with any contaminants at all, you essentially need to remove all the hay, and probably most of the soil it touched, and any that had water pass through the straw and into it. Only extensive testing will reveal if you've gotten it all, but a quick-and-dirty way of assessing toxicity is to deliberately plant some of those things that the indicated treatments are supposed to guard against. If they don't sprout, or if they come up wierdly stunted and die, the soil is still toxic to them.
I'm sorry that this happened, but there are a limited number of options in this case. I would strongly suggest brewing aerated
compost teas and applying them regularly, along with regular applications of oyster mushroom slurry. Boosting the populations of soil organisms and giving them everything they need to thrive is usually the best way to break down toxic gick that can be broken down. Beyond that, if the contaminants are sequestered by a specific plant, then plant that plant, harvest regularly, and have a plan for disposal that removes the contaminated material from your soil food web.
But honestly? I think we would all be well-served in taking the above advice to heart on all our garden beds, lawns, and lands. Living soil has a capacity to sequester and break down toxicity, and in some cases break it down into food. We are exposed to so much toxicity that everything we do, anything we can do will go a long way towards ameliorating our living environments.
Bad stroke of luck there, but don't let it discourage you. Keep us posted, and good luck.
-CK
A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.
-Robert A. Heinlein