Mossy, uneven patchy lawn on (very) sandy soil

You have poor air movement through your turf which is encouraging th

moss. I wouldn't start again because you will effectively ruin any soi structure you may already have. When the ground is dry, push a garden fork deep into the surface t 'open it up' a little. This should be done as many times as is possibl over the entire lawn area. Then, give the moss a good raking over to remove as much thatch a possible exposing some soil, overseed with a good quality dwar ryegrass based seeds mixture, roll well, then finally feed at least 2- times a year. Do not use moss killer on new grass seedlings, it will burn them up. Given that you have very sandy soil which is prone to fertility losse I would mulch all your clippings back onto the ground to recycle a many nutrients as possible. This will also encourage worm activity an keep your soil 'open' to some extent

-- Grassman

I'd go with rototilling the whole thing and starting over. If there are weeds, you can apply Roundup/glyphosate when they are actively growing. Before tilling, spread a few inchs of humus, which could be composted leaves, well seasoned manure, or similar organic matter that is available in your area. That will give you a much improved soil, which will save years of frustration.

Test and adjust the PH as needed. Then re-seed using a high quality seed that is suited for the environment. Apply starter fertilizer and keep constantly moist for several weeks, then gradually back off the watering.

Other choice instead of re-seeding is sod, but of course more $$$