I mow about 2.5 acres that I consider lawn so filling it in with anything will take a lot of material although there are some areas that I think fill will be required. Like where we brought a 22,000 lb lift-all across it to work on the front porch two years ago and it wasn't froze as well as I thought it was. There are still a couple of ruts about 1" deep but the lawnmower bounces pretty good going across those.
I am still thinking about a rigid section spike tooth or coil tooth drag with some extra weight to dethatch and dig into the high spots. It will tear up the grass some but it will re-root over winter and look OK in spring. What I am thinking is that the dirt and roots will be torn off of the high points and deposited in the lower areas but not completely like if I used a heavy blade.
I have been rolling it about every other year with a large roller - 7' x 30" diameter. It is smooth for a while and but then gets rough again. It is generally good topsoil on top of solid clay so there is a lot of motion due to rain and freeze expansion so I expect whatever I do will degrade over a few years and I will have to do it again.
Plug aeration would kind of do the same as the drag but it is not a piece of equipment I have but I do have a friend that has one on the front of a Grashopper mower that he would let me use to try it out. The round plugs should migrate to the low spots and break down filling them in.
I appreciate all the ideas which is what I was looking for. Thank you!
More thoughts would still be appreciated as I have not decided yet and right now it is way too wet to do anything.
Grasshopper makes an Aera-Vator coreless aerator. If that's what your friend has, it won't do much for your issue. They work great for fracturing and aerating, but they don't remove cores of soil.
For shallow tire ruts, I use a potato fork in soft soil. It works best at the end of the season when you don't have to mow any longer, or early spring weeks before need to get the mower back on it. Work along each side of the rut, the full length, gently lifting the sod back up to just above its normal height. I usually stick the fork in several inches and lift that upper layer of topsoil and sod. Now let it sit and the rain will settle some of the loose soil back under the lifted sod and hold it in place. It works surprisingly well.