Soils become compacted because of a lack of adequate amounts of organic matter in the soil, not necessarily from very light traffic although lack of OM and traffic can work together to compact soils.
What soil type do you have? Clay, Sand, Silt?
How much organic matter is in that soil?
What is that soils pH?
How well does that soil drain?
What kind of life is in that soil?
In addition to contacting your local office of the Rutgers Cooperative Extension Service about having a good, reliable soil test done, dig in with these simple soil tests,
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. 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 drains� 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.

to see what you have and what you need to do to make it better.

Thanks for the reply, kimmsr. I'm partway through the tests, and I'll send off a soil test later this week. I had one done a few years ago on our perennial garden, and it indicated mildly acidic sandy loam with 5% organic. That soil had been mulched and amended for years, though.

There weren't many earthworms in the bucket this time--only 2. The soil is also strikingly uneven over the property. Some places have dark topsoil 8" deep, and other spots you hit red clay 2" down. Some spots are builder's sand/gravel. And then there's the occasional chunk of concrete, mostly small. We got most of the large ones already. :)

I'll post the results of your home tests in a day or so. Thanks again.

Thank you for the pictures. You can't imagine how much better that is than our collective imaginations.

You are not overthinking this. You are thinking it through properly. It's just a lot to put down all at once, but I thank you for going to the trouble and not scattering it all over the place.

Your soil is poor and thin not because of anything that has been done to it, but because you have not been using organic fertilizer at least once a year. There is a FAQ on organic lawn care in the GW Organic Gardening Forum. Check that out for a basic primer on the new approach to inexpensive organic lawn care. If you want to improve your soil very quickly, go straight organic and go often.

This year rather than using corn (too expensive) I have been using alfalfa pellets (rabbit chow). When I wrote the Organic Lawn Care FAQ, corn was selling for $3 per bag. This year is was $15-20 per bag while alfalfa was "only" $12 per bag. Alfalfa is a better fertilizer than corn anyway, so it's a much better deal.

I've been on these forums for 10 years. There are two approaches to getting rid of creeping charlie that work. One is to dig up the top six inches of every square inch of the yard and pull out all the roots. Start in one corner and go as far as you can. When you come back, start AGAIN in the SAME CORNER and repeat because you will have missed some. At least the second time it goes much faster. Continue doing and redoing the area until you have nothing but soil. Or the other approach that works is to use non-organic chemicals. I will not address that approach in this forum because this is an organic forum and because the people here are not well versed in the use of the chemicals. If you decide to use something like RoundUp, check into a lawn forum where the members know how to use it. The same goes for bermuda. You can get rid of them, though.

Sand is not a problem in the soil. In fact I prefer sand to anything else when I'm leveling or filling in low areas. If that was your jar test I just commented on, you have mostly sand anyway. Good news there is that sand does not compact like other soils do. Bad news is that sand does not develop a structure like other soils do.

Tree work will not involve equipment. You will get a crew of men who climb trees like monkeys and drag stuff to the front where the equipment is.

Drainage needs to be addressed. You'll need an on site landscaper to fix that for you. For your small lot he might use a tractor with a tool called a box blade or he might just use a group of labor guys. The tractor would be done in 10 minutes.

Dog urine is only a problem when the basic soil is not fertilized. If you had adequate fertilizer down, dog urine becomes instant fertilizer. When you don't have the biology right, then that instant fertilizer burns the roots.

If you are interested in an alternative turf grass, look into the wheatgrasses that might do well in your area. They are normally considered a prairie grass, but when you sow the seed like a lawn and mow it a few times, it looks like one of the best lawns you'll find. Here is a picture of a wheatgrass lawn in Utah.

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He's in a high desert area and waters his lawn beginning in late May or June. Mowing is monthly. His is a mix of wheatgrasses, blue grama, and strawberry clover. When seeding you might try doing half the yard at a time.

At the bottom of your steps you need a landing. It can be a easy as several inches of shredded tree mulch or it could be more formal like a wooden landing or even stone.