I would go with perennial rye but only because it's to late to over seed a whole lawn atm.

I would say about September depending on the weather http://ryegrasses.com/info/whentoplant.html

For top soiling if money is a factor I might go with chemical fertilizer or just a mix of cheap manure and sand m10 to s90% mix you can top soil anytime before or after I wouldn't mix chemicals with new seed.

But it sounds like you need it to be green right now? So we might be able to help with what you have put a few pics up along with your water scheduled and all that.

If you are west of I-5, then you can use one of the Marathon seeds. They come in I, II, and III depending on how slow growing you want them. Higher numbers are slower growers. You could also use Kentucky bluegrass in full sun. If you are east of I-5, then you really should not have a fescue or Kentucky bluegrass. I would call it irresponsible to have fescue east of that line in California. Fescue needs far too much water in the SoCal heat. As soon as you get out of the "morning fog" and on the upslope to the Elsinore Mountains, it's too hot for northern type grasses.

A much better choice of grass for the heat is either hybrid bermuda sod or St Augustine sod. Hybrid bermuda only comes as a sod. It is hybrid in that it is much more well behaved than common bermuda. Seeded bermuda is all common. Common bermuda is what everyone calls a weed, but even that can look nice when properly cared for. Most people are unwilling to maintain it like that for more than a year. If you are going to seed bermuda, you do that in the hottest heat you can get, so NOW. To make the bermuda look good it needs be mowed (lowest setting), twice a week, watered deeply once a week, and fertilized monthly. Any deviation from that and it will thin out or look yellowish. Bermuda only thrives in full sun. St Augustine is a coarse type grass that is much less work to grow. It can be mowed (highest setting) once every 2-3 weeks, watered deeply once a week, and fertilized 3x per year. St Aug will choke out 90% of other grassy plants and many broadleaf weeds.

Before adding topsoil please post a picture showing why you think you need it. SoCal homes since the 70s were well graded for drainage. You don't want to mess that up.

If you want ideas on alternatives to lawns for low water use gardening, you might visit the legendary Roger's Gardens in Corona del Mar. Bring your wallet; they became legendary for a reason.

We belong to a HOA so doing drought tolerant stuff requires hassle beyond belief. We are in Orange, so East of the 5.