I've read this thread a couple of times. I gives me a thought, but it's not an answer or advice. What kept me from posting anything was the part where you (hunter) wrote, "I don't till, so that's not an option for me."
My thought would involve a little tilling. Here's what I was thinking - take the straw out and mulch mow it. Then add that to the compost - mix it together - and then scratch it into the top 3 inches of soil. You would have compost mixed with soil and decomposing straw.
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