Did you write this post or did I ?!!!!
My lawn is also a mess [brought the house over the winter so gradually reclaiming it]
I brought a scarifier with a friend from BnQ, brilliant toy, loads and loads of moss brought up by that, masses more than you could ever rake up. Today I went over the thing with a hollow tine fork. You could probably do it with a regular fork too, the tube thingies on the hollow tine clogged up easily, but it was still making holes [probably by compaction, but holes at least] and they were bigger than a fork would make. Then tried, not very successfully, to brush sand into the holes. Next is to weed out all the buttercups and finally seed the many bare patches[swathes]
No idea yet if all this will work, but the books say to do it this way
. I did read about mixing the grass seed with damp sand and 'pre-germinating' it, so may give that a go. With kids, dogs, chooks and lots of wild birds, I figure the seed needs to take as soon as possible to get established.
Just aiming for green ground cover, that isnt creeping buttercup. Well anything green would be good as keeping 3 kayaks on the lawn for several months has killed off what the moss didnt get first !