If your garden is on a hill why not build a stair stepping raised bed for your tomatoes?
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Californian

The insect damage would probably be less severe if you staked your plants, though you'd still have some that got to your fruits by flying. And maybe you'd have fewer rotting tomatoes on wet soil if you staked them.

I gardened for many years and let my tomatoes sprawl and they did just fine. These days I just don't have the room and much prefer picking tomatoes that are held on upright plants.

I hear you about cage storage. I don't know if it would be useful for you to try or not, but I use staked lengths of cattle panel and/or CRW and then just tie the growing plants to the wires. I alternate the plants on each side to distribute their later weight and to give the roots a little more room.

Then the only thing to store in the winter is the flat panels against a wall or somewhere else out of eyesight.

I like the idea of terraces for your tomatoes if you can do it. They'd give water a chance to seep down toward the roots before running off to the next level.

There are ways to get your tomatoes off the ground other than cages, which I agree take some significant storage space. I like the link below because there are lots of pictures.

The other thought I had is that you can grow determinate tomatoes which are bush-like and don't need staking to stay off the ground.

Here is a link that might be useful: Many Ways to Support Tomatoes

You might want to try drip irrigation. I garden on a hill, and the drip irrigation is slow enough that it doesn't all run down to the bottom of the hill.

Pure clay soil on a slope sounds like you need an alternative.
(Or skip fighting with the variables you are encountering & go with the cherry toms that did well).
I can't take any credit for the methods, but suggest you investigate different options of container growing for tomatoes.
This way you can use an appropriate medium, achieve water control, directly target fertilization & get off the ground for a better chance to manage insects/diseases.
GW has a forum on Container Growing talking about how to use recycled 5 gallon buckets & also, Raybo posts there about the productive Earth'Tainers.
(Wish I could claim I was that inventive & impress the females.)

" My biggest problems are blossom end rot, sunscald, vines withering, and tomatoes rotting before they ripen. "

Almost every problem is somehow related to what we feed (nutrient) our plants!

I grow strawberries and TOMATOES only. I grow hydro, by the way. Just the same, if you'll up the calcium you're feeding your toms, the blossom end rot will come to a screeching halt.

Sunscald and vines withering can be caused by a couple of different things: Of course, no water is one! The other is a little bug that eats at the base of the trunk. This causes rotting and throws the plant into a tizzy.

Getting your foliage OFF the ground is a must and DO NOT water at night or in the early evening. Watering at night causes mold and mildew and other wet-nasty problems.

I place a pole at each end of my tomato rows and string a cable or 1 x 2 board across with ropes hanging from it above each plant. I then tie the growing plants to the rope, enabling them to "rest" on the rope for support. This keeps things off the ground.

Another thing you might consider is "Super-cropping" as well as single-truss harvesting. No room here to explain the last two things. Email me for that from my profile. I live just to the south of you in San Diego, by the way!

I had an idea once but I never carried through on it. I bought thirty used 55 gallon plastic drums. I was going to cut them in half, and cut the top and bottom off them so I would have a bunch of open ended plastic cylinders about two feet in diameter and about 20 inches high. I was going to set them all over the slope of my hill, with them set so they were level on the sloping hill. I would then fill them almost to the top with planting mix. I would plant one tomato in each one. Since the top of the cylinder would be about 18 inches above the surrounding soil, the vines would cascade over the sides down to the ground, but most of each vine would be in the air so I wouldn't have roly poly damage to the fruit touching the ground. Watering would be a breeze, just put an inch of water into each cylinder every couple of days. No more weed problems either. And since the bottom of the cylinder was open the roots could grow down into the soil if they wanted to. But then I found out I could sell the barrels for three times as much as I paid for the thirty barrels I had so I sold them.

" My biggest problems are blossom end rot, sunscald, vines withering, and tomatoes rotting before they ripen. "

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It seems to me that you need to make some diagnoses first in order to understand what's going on.

And having grown over 2000 different varieties, most of them by sprawling, I can't see that any of the above would be directly related to how you grow your tomatoes. I have quite a few friends in S Cal and they also grown theirs by sprawling as long as they don't have a Root Knot Nematode or Fusarium problem in their soil.

Questions to ask are whether the wilted plants are wilting due to lack of water or due to systemic diseases such as RKN's or Fusarium, which are a problem for lots of folks in s Cal. Or are you dealing with the more common folaige diseases that can be found almost everywhere. The latter are not usually associated with wilting, though.

Are the rottinmg fruits only those fruiits that make contact with the soil? Or are the plants so close together and humidity high from irrigation that the fungi and bacteria known to infect fruits under those conditions are the problem.

Sunscald is usually due to lack of adequate foliage cover and/or exposure of fruits after harvest has started and rearrangement of the vines.

BER is a complex physiological problem with many variables and right now there's lots of other issues to attack, but you might read the article on BER in the FAQ at the top of this first page.

Finally, and I think the most important, is when you're growing your tomatoes. Almost all my S Cal friends grow two crops a year b'c trying to keep plants going thru the hot summer and get decent fruit set is not a good idea. So growing two crops a year I think you might consider.

Hope that helps.

Carolyn