Fertilisers for damaged/reseeded lawn

Rather lazy gardener here!

We have three lawns, two small ones we laid ourselves following landscaping around 10 years ago, they are OK, certainly good enough for our needs, there is a bit of moss and weeds, but grass is still in the majority.

The third – main one around 250m^2 is not so good – this is in a dip, so is fairly damp, been there around 25 years (before we moved in) and has not been cared for – we have mowed perhaps too infrequently, and done nothing about the moss problem which was there right from the start – but which has now taken over completely!

We have decided to sort it, so have done a partial removal of moss (scarifying/raking) and applied ferrous sulphate  - now the lawn is totally black (although surprisingly there are still some green patches of grass!), in a week or so we will scarify again – hopefully getting right down to the soil with a removal of all the moss and thatch, re apply the FeSO4 then repeat – planning to scarify again into the top layer of soil so in reality we will end up with a pretty baron “lawn”.

We are going to pre-fertilise with “kiss my grass “ pre-seed (6-9-6), then over seed with Boston seeds “childs play”.

We don’t plan to use a spring feed as we will miss the boat; by the time we come to applying any fertiliser – spring will be long gone!

So now the two questions:

1)      Will it be worth applying a spring/summer fertiliser – even though the grass would really only be a few weeks old by summer?

2)      In the Autumn, we may plan on using FeSO4 again if the moss starts showing signs, although probably at 3gm/m^2 rather than 5gm/m^2. However we are intending to apply a winter fertiliser – something like 6-5-10 +Mg, or 3-10-5, - but can’t decide which is best – the higher phosphate to promote the roots or the higher potassium to harden the grass?

Effectively this would be more like a new lawn, as there will be little of the old left, but it won’t have the clean-start of a true new lawn, and it will have the strain and damage of all the work we have clearing away the moss – chemically and mechanically.

We are ordering stuff so are planning to get the fertiliser at the same time – saving on postage – hence the early questions!