We deal with the same problem on occasion, depending on rainfall, fields adjacent to wetlands, varying times of drying weather etc.
I would agree with Allen, just don't try it until it dries, if not this fall, you may have to wait until spring. It may be possible to over seed, check your PH, fertility, and address same, being you are in there already.
Another tactic that I use is to surface drain it, if its trapped water, best thing you can do is to get it to run off. If the affected areas are surrounded by drier ground, often times using a loader bucket, I can flatten the areas, even if I run through it, ideally you try to reach in from dry ground, but even if wet, you can even things out so that water will run off in some cases, instead of letting it get trapped. Ruts become problems because they hold water and make surrounding areas wet. The philosophy in doing this is to carefully work your way out and do so with minimal passes or tracking through it. Not for everyone, can easily make a mess too LOL!!!
Now if you are talking large expansive wet areas or its just inundated end to end, you obviously can't go out there with wheeled or track type tractors. I've always had good luck doing this in smaller areas, it always looks worse than it is. Once I've flattened or minimized the ruts, I just leave it be, sometimes patch-seed if needed, but clump grasses like orchard, timothy, (which is or is not clump, I forget) always seems to come back and you won't see any disturbance. What I don't like about not seeding is that undesirable seed or what have you now may have a great spot to get a foothold in a particular field. Not too many kinds of weeds will invade orchard grass, milkweed, and 2 others I have seen here in a field of it that has been sod since the late 60's, golden rod can take over if the field is not cut for several years, I've seen new stands planted, cut for a few years, beautiful stands too, then left idle, right back to golden rod, like if you planted it. Funny thing about that is, often times nothing but goldenrod grows.
Many people may disagree, fooling in the mud or a wet field can be a total waste of time, all depends on the soil, moisture, access, experience, equipment and underfoot conditions, some places top soils are deep, then clay and so on, nothing good to bear on, that is when tractors and equipment get buried easily, just making a bigger mess and more work. Some places you may have 1 or 2 passes before the water pumps up and that's it, so you have to make it count.
My experience with working in these conditions comes from being a dozer operator, and or other earthmoving equipment full time for several years. One of the most common tasks to perform was working in wet conditions, and keeping the site or work areas well drained. Always on the surface, getting rid of ruts, ponding areas etc., difference here is site work jobs are mostly dirt, it requires a little more attention if you are fooling with it in grass and trying to minimize tire and rut disturbances like you mention. As a dozer operator, you learn quickly how to deal with wet conditions, some you can work, some you may lose a tractor into deep suction/mud, and sometimes, you may hit something unforseen, I did it with a D8K once, traveling from one work area to another in a 100 acre flat field being converted to a subdivision, place could have been a landing strip, they raised sod over the next hedge row. The D8K, just sunk on one side, trapped water, well thats a big ole heavy crawler, surface did not look any different.
My inclination would be to use a loader if I could get near it and its not deep organic/non bearing soils, flatten and leave til spring, spot or patch seed, or wait til spring and it dries, disk the effected areas, cultipack, seed, then pack again, if you seed then pack, might be too deep for the seed.
One of the reasons we would try to avoid replanting a decent stand of hay grasses is all the work to do so, lots of rocks in the soil around here, its nice when you don't have to do tillage and bring them up, then deal with removing them.
