Six inches is pretty thin. Tomato roots can grow a foot or two deep. I suppose if you keep the plants well spaced it could work, but you'll be watering a lot.

I've never worked with gumbo, but I'm familiar with Southern clay (the kind of clay that makes you an inch taller with every step you take :).

I built raised beds -- 8" tall -- and started amending them in early fall by digging in tons of shredded leaves, grass clippings, straw, bags of coffee grounds collected at Starbucks, and some manure. I kept repeating this process every month or so as the soil level went down. By spring it was still very chunky and wet but usable. That first growing season was pathetic, but I kept digging in more shredded leaves (free from my trees) and coffee grounds (free from Starbucks) and after about 3 years I got black friable soil about a foot down. Then things improved dramatically.

So I think you are on the right track, but if you want to grow this summer, you probably should have started in the fall. And be patient, you may not see results for a couple of seasons.

I plan to space the tomatoes at least 18" if not 2' apart which should provide plenty of room for each. Most will be an indeterminate variety of a cherry tomato but will also try some shorter/bushier varieties as well. I will probably amend just the clay using lime until I reach a crumbly texture and then add the other amendments followed by a top 8" layer of good garden soil enriched with mushroom compost for this growing season and then replenish with a mixture of composted grass, leaves and well aged manures between each growing season thereafter.

I'm not sure what you expect the lime to do as a soil amendment. Other than altering soil pH, it will do nothing to make clay assume a more "crumbly texture". That is only achievable by the incorporation of organic matter. It is also NEVER advised to add sand to clay.....unless in high quantity, like 50% of the volume. Anything less and you are more likley to end up with adobe, not anywhere close to a workable soil!

Lime is great for loosening clay soil as it helps break molecular bonds holding clay particles together. An old method that still works.

Your plan for wide spacing sounds smart. Now, I'm assuming the gumbo layer is impenetrable. If I were you, I'd dig into the gumbo itself and amend with compost before putting the raised bed on top of it.

I'd be careful about lime. Gumbo soils are usually alkaline, and lime would be somewhat toxic. Before you use lime, get a handle on your soil pH.

The benefits of adding lime are up for some dispute. Lime solidifies clay soils - hardly something one would want when developing a raised bed soil. It is used primarily on construction sites to provide a stable base for both equipment and paving or foundations and embankments.

That's right about sand. Sand loosens gumbo/clayey soil if used in VERY large quantities. As in 1:1. Smaller amounts of sand mixed with clay make, well, concrete.

Whether or not lime would help in a "clay" soil (without testing, one would not know if it's clay or not) would depend on the ion balance as it exists. There's no blanket statement that would apply.

In the case of a misbalanced, calcium-low, magnesium-normal (to Mg-slightly-heavy) soil, calcium will help a bit to loosen your soil just by altering the ionic balance and binding between soil particles.

Other than that, it's not so effective and you should look to other methods.

However, blanket statements that calcium does not work are wrong.

But again, I'd do a jar test to assure that you have clay in the first place (not, I suppose, that it really matters, but I thought I did for some time. Turns out it's 98% silt).