You don't say how much organic matter you're adding.

So, guessing that you're like most folks, I'll suggest that you're not adding enough.

Continue adding compost. Perhaps add 4 inches (but 2 inches at a time) the next time you plant the garden.

Then mix in 2 inches more during each successive season.

And you can also grow a cover crop during the off-season which you'll till in before it blooms, and at least a month before you plant.

As for tilling, it's worth knowing that rototilling a lot should be avoided because it breaks down any soil structure that does exist.

Till only enough to mix in the organic matter, just one or two passes.

If you add sand, make sure you add enough. Adding too little can make it worse. You need to add a lot of sand before it helps. I've read that you need to have at least 45% sand.

The disadvantage of sand is that it takes so much. The advantage is that it makes a permanent change (organic matter needs to be replaced on a regular basis).

Till in expanded shale and mulch the bed. And keep adding compost because it takes quite a bit to completely change clay soil.

Concentrate on adding organic matter. To make any difference in clay most all of the state universities will tell you that you need to add 45 percent sand, and that will get expensive. Cornell and the University of Washington will tell you that you need to add 75 percent sand. Expanded shale is no better.
To get enough organic matter into the soil does take an initial infusion of lots, but if you are in an area with lots of deciduous trees you have access to tons of material to use.

Thank you so much, everyone, for taking the time to respond to my question. I appreciate all of your input and am hoping for a garden next year with improved soil. Wish I could send you all some of my sun-kissed tomatoes and delicious green beans!
Fiesta

The past few years, I've been mulch mowing the leaves from my trees into the lawn, but gathering leaves from neighbors and layering leaves and coffee grounds from Starbucks on the garden to a depth of about 3 feet. By spring it is usually down to about 6-12 inches deep. I'll plant directly in that or put some soil on top and plant in the soil. That approach works best for things like tomatoes and peppers that have already been started. For rows, I'd probably move the stuff aside and plant in the soil, leaving the leaves and coffee grounds as a mulch.

My soil has gone from nearly impenetrable yellow stuff with no worms to very soft crumbly black stuff that is just full of worms.

You could also plant a cover crop of green manure. I'm growing buckwheat right now and it will be cut and tilled under soon. I chose it because it's a quick cover crop, but there are many things you could plant as a green manure crop.

After the cover crop, I'm going to do what bpgreen suggested and layer compostables in the same area - hopefully to have a richer planting area for the spring.

you are talking about 150 sq ft garden, it ain't gonna take THAT much sand. around here the ratio is 50%. but it depends on just how much and what TYPE clay you have. red clay is already sandy so you use less, while our blue/grey clay has very little sand. i don't know about your area, but i can get a 12 yard truck of sand delivered for around 100.00. they will even dump it in several piles for you.

for our clay if you want 6 inches of good topsoil, you need to add 3 inches of sand to the top and then till to a 6" depth. if you want 12inches, you add 6". eitherway, the effect is immediate and PERMANENT. adding organic mus tbe done every year.

i recommend doing the sand and still add in organics annually to keep the soil healthy.

fiesta, as I understand it, you see your problem as "the soil still cracks and is hard when it is dry." The solution is to cover the soil with mulch, a cover crop, and close spacing of plants. Clay soil is wonderful and full of minerals. It holds water well, so you don't need to water as frequently. Rather than buy a truckload of sand, I'd go for bpgreen's approach, especially if you don't have a winter garden: cover the soil with a few feet of organic matter.