A basic rule I used to follow was that if the lawn was more than 50% affected by whatever maladies, consideration should be given to replacing the lawn.I feel that you may need to consider doing this, then you can sort out the causes of your bad lawn .A compromise would be to add loads of v.sharp sand, this in time will help improve your drainage and by so doing deter the moss from developing, with the applications of shade tolerant seed (from a seedsman) you should eventually have a lawn to be happy to roll around on!!