Sit down because I'm jumping right into some science. This is for your husband to help understand why the bridge idea is not going to help you. Normal soil has an open pore structure that allows air and water to pass through it. Inside this structure lives 10s of thousands of species of beneficial microbes which thrive on the open pore structure. These microbes are Mother Nature's invention. As it turns out the species of microbes living in swampy land are different from those living in dryish land (lawns). When you allow standing water to stand for several days, that cuts off the air flow to the beneficial microbes and their populations begin to decrease. If this happens enough, normal grass will thin out and stop growing. They will be replaced by swamp grasses like nutgrass and some others. So it is important to keep the water from pooling on your lawn. Back to the issue... If your community has an ordinance that says homeowners must drain all water from their own property and not allow it to cross over onto a neighbor's land, then all you should have to do is call your city code compliance officers and make them deal with it. If you live in the savage west, then you might have to do it yourself. Talk to your neighbors and ask them to berm up their land at the fence to keep the water on their side. Since they already dug the ditch, they are unlikely to bend to your wishes. So when that doesn't work, berm up your side of the fence and push their water back onto their property (see how they like having standing pools of water!!). Six inches of berm would normally be plenty. Planting a lawn in the spring is not the best idea, but if you really have to you have to. If you can afford sod, then that should be better, but if you were planning to seed, I would not spend a lot on seed for a spring installation. What will happen is all that new grass will find itself competing with crabgrass which also sprouts in the spring. Your grass seed will be less hardy than the crabgrass and will thin out in the summer heat. It is not uncommon to have a full crabgrass lawn by July. It is much better to seed new grass in the fall because crabgrass seed is not sprouting then. It also gives the new grass all winter and spring to develop heat tolerant roots. Now a word on forum etiquette. This is not your thread. The original poster had a problem with soil structure. Your problem is neighborhood drainage. You should have opened a new topic so people who want to help you don't have to read through someone else's problem from last year - which is really not your problem. I also suspect you will need some advice on planting your lawn (spring? or fall - either one). Now is the time to ask, so post a new topic! When you ask about planting a new lawn, please mention specifically where you live. The zone system is not good for helping with lawns, so give a town or zip code. And if you want more help on the neighborhood drainage issue, I would still post a new topic with your new questions. This forum seems to have a lot of opinions about neighbors '-)

Also for watering: the soil looks too dry too soon currently. Mine, too--and I have no real problems. The very top surface of the soil dries out really fast in sun and wind, but that doesn't mean there isn't water underneath. You can test that by pushing a screwdriver into the soil. If it goes in fairly easily (barring rocks), your soil is damp. Or drive a small trowel into it and separate it into a V shape by rocking it a little bit. That'll give you a direct visual on how deep the water is. Here would be my plan: for now do very frequent waterings to help really wet the soil, I'm not familiar with California (except for the part about moderate temperatures and no rain), but this doesn't sound like a good idea--it encourages shallow roots and lawn diseases. The standard is 1" of water a week, all at once (well, within a day to allow for on/off cycles to allow the water to penetrate). For sandy soil your mileage will differ because the water wicks out fast and goes very deep very quickly. I will also probably try milorganite as a jump start, as I fear my soil is probably pretty depleted. I swear by it, others don't (it is processed sewage, but heated enough to kill everything in it). The 18 lbs/thousand square feet I put down last weekend kicked in and it's a rainy week. The grass, since Sunday, has grown one and a half inches and gone a deeper green. Once it stops raining, I'll mow. I went high, but I'm going to renovate this fall--with a deep, heavy core aeration I want lots of organics mixing into the holes. I alternate it with alfalfa and soy. When I started (early last year), my soil profile was slightly silty clay, poor drainage, very poor water penetration, hard as a rock, and a light tan. It had been corn field for as long as I could remember prior to building, and even my parents don't remember when it wasn't. Call it 40 years of abuse. Now it's still slightly silty clay (nothing's going to change that short of a renovation down to a foot or more). Drainage is fair to good, penetration is good to excellent, the soil is still hard when dry (it's supposed to be), but spongy when wet. The top half-inch is black, another inch is deep brown, and a good three inches below that have turned a midrange brown. Everything grows better and more strongly. I'm very pleased. Some older photos are here. I have to update them--the grass has improved since these were taken and the season advanced a bit.

Post pics of the entire yard, looking out from the patio as well as toward it from the far side. Are the neighbor's yards higher or lower, or is it all fairly flat? What kind of soil is that (under the sand you added)? I really never thought TX would be wet enough to need French drains!

Another vote for the PVC. Ask your landscapers for suggestions on how to handle the issues you are concerned about at the drop off. I can think of about three different methods to deal with that, off the top of my head, but one would need to actually see the site to fix on the best method. The best method is probably as Sofaspud mentions, terminate into a dry well. Once you trench, slope and install the PVC you are done. Any other solution presents ongoing maintenance issues of varying degrees. Whatever you do, do install a clean out somewhere close to the house so you can "jet" your hose into it periodically to wash out debris and critter nests.