Welcome to the forum, Christie!
I'm no expert on lawns, but when we bought our place 4 years ago, the back lawn was 90%
weeds, and half-way up to my knees. I can't use
weed and feed, due to 2 children, 2 rabbits, and 2 cats. I've adopted a long- term approach, where I put up with the
weeds for a while. I have found that in winter the
weeds do take over a bit, and in summer the grass starts winning. Constant mowing seems to help by stopping the
weeds from seeding (the grass we have grows with runners). Also, loosening the soil and planting heaps of grass
seed works for me, but you've already been doing that. Don't know about tilling it up; sounds like it should work.
The compost is a good thing, and some gypsum would help break up the clay also. Winter is a great time to prepare the beds.