[Begin: Soapbox rant]:
Who are the idiots who came up with 10 minutes per zone, 3 days per week? Wait! Let me guess. It was the Water And Sprinkler Timer Electricians (WASTE). Or the Sprinkler Installation Society of Southern California. If you want to save water and have a minimal shot at growing grass (to keep the weeds out, to keep the dust down, to moderate the temperature, etc.), then you should water for up to many hours per day but only once every week or two. San Antonio has an "enlightened" plan like that. I wish I could say I had something to do with that plan, but it really works well. We are also allowed to use a soaker hose. If you know how to use a soaker hose, you don't even need sprinklers and will end up using a lot less water. I've heard some pretty dumb restrictions, but that is the worst yet.
[End: Soapbox rant]

NEVER ROTOTILL in preparation for sod. That is why you have such a bumpy surface today. Sometime in the past someone rototilled it and it has settled unevenly. It happens every time unless you have a rototiller mounted on a tractor. Only professional sports installers use that equipment. So just put that out of your mind. If you have an uneven surface, you can level it. Search this forum for leveling to get some ideas. Then if you still have questions, come back with those separately.

The grass you really kinda need is common bermuda. Since your water restrictions will eventually kill every kind of grass, you may as well plant one that will come back for you when you get a week of rains.

For most of the country it is too late to plant bermuda seed. For you in Oceanside, there is never a great time to plant it because your high temperatures are never high enough for bermuda seed. But I'm sure it will sprout and grow for you if you put it down. You can probably still do it this year and get as good a result as if you did it somewhat earlier. Ideally I would tell you to wait until next June or July, but I think this will work for you.

Seed with a mixture of Yukon, Riviera, and Princess 77 at a rate of 3 pounds per 1,000 square feet. You can find those seeds online at Douglass King Seed at dkseeds.com.

Here are the general guidelines for bermuda as reinterpreted from The Bermuda Bible

Every month during the growing season
Fertilize with a high N fertilizer

Every week during the growing season
Water a full inch, all at one time
Mulch mow 2x at about 2 inches high

Before you seed you should kill everything with Round Up. Spray it once and water for your piddly 10 minutes per zone all three days in an attempt to sprout more weed seeds. After a week of that, spray again to kill anything that is still alive. Then you can rake up all the dead grass and seed. Maybe wait a day. Roll the new seed down or at least walk on every square inch of it. You want it to make good contact with the soil. Then you might need to get a temporary waiver from your local people to water 3x per day, every day, for 2 weeks. Mow when the grass is up to 2.5 inches. You can start the monthly fertilizer after your second mowing of new grass. In Oceanside if you water according to your guidelines all winter long, and keep it fertilized, it might remain green and growing all winter.

If you follow the monthly fertilizer schedule, you should add an addition application of organic fertilizer at least once per year. Your soil microbes need this booster so they can process the chemical fertilizers. Or you could to 100% organic. If you don't do any organic and repeatedly hit the soil with chemicals, you'll deplete the microbes and reach a point where the chemical fert doesn't seem to work as well as it used to. That is when your microbe population has crashed and you have "unhealthy" soil.

Very thorough and helpful. I will look into options for re-leveling. I'm actually glad to hear that rototilling the whole yard is a bad idea... that's a lot of work.

I imagine a few loads of topsoil and compost would do the trick.

Just a quick follow-up: Can I just stop watering the lawn in order to effectively kill everything off, or will weeds lay dormant until watered?

Like I said, a good portion is dead already so this would save me having to mix and apply all that roundup. And how heavy of a raking should I give it once all of the grass/weeds are dead? Do I need to remove any/all thatch and dead clumps or will the new grass set seed on top of it ok?

Thanks again, that was very helpful.

Bringing in a load of topsoil will always change your drainage. This is fine if you already have large areas of low spots where water collects for hours or days when it rains. If you don't already have that, then bringing in topsoil often creates those spots where you don't want them. What would work better is bags of topsoil or sand. Get more than you need to fill the holes and return the unopened ones.

Compost doesn't fill anything. It provides temporary bulk until the soil microbes consume it.

If you stop watering it might kill the plants on top but the seeds remain. If you spray with Round Up now, for example, and watered daily for a week, the RU would kill the existing plants and the watering would sprout all/most of the new weeds. Then in a week you could spray the RU again and feel confident that you got all the weeds fit to kill. Then rake up all the dead stuff and plant on the bare soil. You need to have good contact with the soil and seeds for good germination. You could use a power rake, slit seeder, or any device with vertical cutters that can be adjusted up/down to just touch the soil surface. Those things can clear all the vegetation out. Instead of raking, once it's up and fluffy, you can blow it away with a leaf blower. That sounds easier but it isn't always. Plus it's always dusty when you blow.