The plan was to rent a sod cutter to remove what is living there, lay down a layer of cardboard, have compost delivered, rent a roller to compact it, and then seed and proceed.

I am a lawn noob though so am just checking to be sure we are doing this "right."

Unless you need to get rid of excess soil, I would not use a sod cutter. Is your soil level higher than adjacent hardscape like concrete?

Cardboard and compost will get you in trouble. Here's a reasonable approach. Feel free to modify it based on your thoughts and others posting later.

1. Kill all vegetation with something like RoundUp.
2. Water it good and a week later, kill it again with Roundup.
3. Scratch only the surface deep (1/8 inch) with a verticutter, power rake or slit seeder and remove all the dead material.
4. Seed
5. Roll seed down into the soil (don't cover it).
6. Water every day, 3x per day, 10 minutes each time, for the next 3 weeks or until you get 80% germination. Then start backing off on watering frequency.

Cardboard might stop a weed or two but it will also prevent the new seed from rooting properly. Compost serves no purpose in seeding although after the grass is up, it can have limited positive side effects. I'm kind of a lone wolf on downplaying the benefits of compost. I garden organically and try to avoid compost for the traditional uses. I mulch with it.

The grass is only slightly above the grade of the driveway so we could knock it down with some creative shovel work if necessary.

My only concern was that I was hoping to introduce some organic matter to the soil. Below the level of the roots, there is literally nothing but sand. Our whole lot is this way and grass dries out very rapidly making keeping it alive without watering every day( past when the lawn is getting established) difficult. Is there an effective way to incorporate something that will hold moisture and nourish the grass?