Perhaps a few thoughts for you to consider..
Hay is a hot green material.Manures not aged over a year pending on the animal source can also fall into the hot category.chicken, sheep, rabbit, horse are all warmer manures..Goats if they are
dairy producers a bit cooler then if they are not producing
milk or babies.Cows the same dairy cow or growing calves are less hot then animals like steers for meat production.But still a cooler pile of manure..Pigs are a cooler manure as well.
Alfalfa hay is a hotter hay then say a timothy grass, one would
feed their horses.Alfalfa is a great garden additive but usually not unless it has been composted or is in a powdered form such as alfalfa meal or such.. Because in the hay state it is hot when it breaks down but also a higher nitrogen then baby plants care to be surrounded by,, even in a cooler climate like mine..LOL,I once tried it to
boost the heat for my babies trying to get a push on the garden season,, Notice it says once,, LOL
Hay also is very weedy, meaning it comes with not only some weed seeds but also the type of plants that it is cut from which people often consider weedy when they take over the beds.Worse yet if you happen to be certified weed free, it is most likely been hit with a nasty chemical which you may not wish to have doing a break down in your gardens.If residues are present from this it can also deter the development of your crops.
I rarely use hay products with in my gardens, unless I am needing a hot green for the compost.Straw has always been my preferred mulch as well as gardening medium these days.
My suggestion would be to pile this all up and make a hot compost pile through the summer.. The heat generated should be enough to kill weed seeds as well as break it down into a nice compost material that the plants would have a preference for.Another method if you have the space would be to do a sheet garden with it that is not used this year but next year after it has had time to cool down and go through the weed sprouting good time it can become..
Or if you have the space another would be to layer it into the
lasagna type beds,, this would be considered a hot green so it would need layers of cool browns such as leaves, soil, peat, old wood chips etc,,If you did this and let it sit for the summer it would be usable for the fall and great planting for the spring.
I see your looking at Huglekultur it would be great in that sense as it will break down nicely when layered in to create a nice bed of soil and would balance the nitro sucking from the wood break down..
Any how just a few thoughts from our gardens to yours
Alan Westerman Memorial gardens
AKA
the Happy House Teaching Gardens