Call local farms to ask about taking away their manure for free. Most of them will be paying $5-$15 per cubic yard to have it removed. Ask if their removal service can deliver to you. If not, call contractors to ask about cost of them loading and delivering (or just delivering, if loading can be done by the supplier) some dump truck loads of manure. To cover 40x90 feet with 6 inches of manure, you need 22 cubic yards of manure, which is about 4 dump truck loads.

Soil that is compacted lacks sufficient organic matter, so the solution is to add lots of organic matter. Manure is one, small, part of that. Compost would be better especially if the manure that would be worked into the soil is properly composted first.
The people at your local AgCanada office might be able to help you find a good lab for a soil test for pH and nutrients and these simple soil tests can help guide you toward making a good, healthy soil.
1) Structure. From that soil sample put enough of the rest to make a 4 inch level in a clear 1 quart jar, with a tight fitting lid. Fill that jar with water and replace the lid, tightly. Shake the jar vigorously and then let it stand for 24 hours. Your soil will settle out according to soil particle size and weight. For example, a good loam will have about 1-3/4 inch (about 45%) of sand on the bottom. about 1 inch (about 25%) of silt next, about 1 inch (25%) of clay above that, and about 1/4 inch (about 5%) of organic matter on the top.

2) Drainage. Dig a hole 1 foot square and 1 foot deep and fill that with water. After that water drains away refill the hole with more water and time how long it takes that to drain away. Anything less than 2 hours and your soil drainsâ too quickly and needs more organic matter to slow that drainage down. Anything over 6 hours and the soil drains too slowly and needs lots of organic matter to speed it up.

3) Tilth. Take a handful of your slightly damp soil and squeeze it tightly. When the pressure is released the soil should hold together in that clump, but when poked with a finger that clump should fall apart.

4) Smell. What does your soil smell like? A pleasant, rich earthy odor? Putrid, offensive, repugnant odor? The more organic matter in your soil the more active the soil bacteria will be and the nicer your soil will smell.

5) Life. How many earthworms per shovel full were there? 5 or more indicates a pretty healthy soil. Fewer than 5, according to the Natural Resources Conservation Service, indicates a soil that is not healthy.

Soil that has been physically compacted needs to be physically uncompacted that takes equipment or muscle power never drive or even walk where you have tilled

Wood chips are a free source of organic matter and have worked well for me with just an extra sprinkle of nitrogen the first year

I have seen severally compacted soils loosened simply by plunking sufficient quantities of organic matter on that asoil and leaving it there for some time. Not nearly as fast as mechanical aeration but your soil bacteria will, if allowed, do remarkable things to correct your soils problems if you treat them right.

Deep-rooting plants in addtion to the always-suggestion of organic matter and compost might help. If not too late, a cover crop of some sort might be of assistance. There are various seed mixes sold and designed for this sort of thing and for different sorts of soil conditions. Don't know what's best for your area for this time of year but I'm sure there is a company that wants to sell you something.

The writer has told us that a tractor has been driven over the entire area. That is the reason the soil is compacted, not because of any loss of organic matter.
Putting organic matter as she has already done and tilling it in, then having a tractor's weight go over that, speaks to me that it is that which has compacted it, not any loss of organic matter.
If one wishes to wait for a worm to uncompact a plot of land, one should then bring out either the book War and Peace or start sewing sweaters for the troops in Afghanistan.

Compacted soil can still be turned over with another tilling and IF the soil proves out to be needing help of organics, then she can do that at that time.