my opinion its your best option. i would do it now but i would mix in some winter rye. the rye will stay green though the winter and die out when the fescue kicks in. if these grasses wont work in your zone just check with your local garden center to see what you could sub.
I would let it sit till spring. The freeze thaw of winter will probably take care of the problem by itself. Plus, it's probably still green in the ruts. Fill it with soil and it will be an eyesore all winter. My bets are that by spring you won't need to do a thing.
We repair ruts in commericial property by taking a pick and pulling the soil back up. You can avoid damaging the soid in this manner. Essentially you are "unpacking" the soil where the truck ran. Then after pulling the soil and sod back up you can put a small amount of sand/soil to fill in the cracks. Works great where the big trucks run across lawn constantly.
I agree w/ ed2hess. try using a pitch fork like you would for a ball mark on a green in golf. Works great and if you do it right, you won't have to fill with anything. I've done here at the college many times and it works well.