I would suggest double-digging, but 40x40 is a lot of work, not to mention additives. So how about double-digging sections within that space? Dig waaay down, pull soil up and mix in wheelbarrow with sand, fertilizer/compost, potting soil... and put this amended soil back into the hole/section. The spaces between would be lasagna. Over a period of years, the whole bed would get this treatment and improve tilth of soil.
One other idea that has worked well for me ... make a 'cone'[in bed] of fertilizer and add earthworms to the cone. I add pureed kitchen scraps to sides of the cone. Top off with UCG and coffee water. My 'cones' are teeming with earthworms. I went from hardly any earthworms in my garden beds to tons of these little earth movers.
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I'm doing this slowly and love it!
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