Next time you weed and feed, rake the lawn once the weeds and moss are dead and get all the dead material off the lawn then go over it with an aerator, (you can hire mechanical and powered thatch removal and aerator equipment) spread lawn sand and then spread that mix of seed and nutrients you can get to reseed the lawn.
Alternatively do what we did we did. We contacted one of those grass care companies, you see their little vans every where and they have names like Green Care, Green Sleeves, Green grow the rushes O etc. They charged £150 for their first visit when they dethatched our very large lawn (50ft x 100ft), aerated it and weed and fed it, good half days work. They now charge £50 once a quarter to give it a weed and feed.
Our lawn that was 50% moss, 50% max grass is now, green and 100% grass. Between visits, if any big weed like a dandelion appears I spray it with a spot lawn weeder, otherwise I leave it to the two nice men that deal with everything else to do with the lawn (except cut it) for me.