What will really help here is follow my advice but before you lay down the wood chips, plant some daikon radish seeds into the compost/biochar/manure mix. You do not have to plant deep!

These will drill channels down into your soil and scavenge nitrogen and nutrients from the manure.

If you cover this with woodchips, go easy, only an inch or so, so the radishes can find their way up to sunlight.

Next spring when you kill them (by chopping the tops off), as the radish decays, your compost/ biochar/manure mix well fall into the channels and begin to deepen yor soil!

On my soil here these guys will go down 6-9 inches and most winter kill.

Here is where I get my seed