As mentioned above, don’t screw up your plumbing lines or furnace.
From this end of the internet, I couldn’t tell you if 18” in from the existing footing is enough to prevent undermining, or if it is overkill. It depends on how much deeper you are going than the existing, and also on soil conditions that shouldn’t be speculated upon.
In Seattle, you should spend a lot of time thinking about moisture, as RdSnt mentioned. How high is the water table on your property? Also, if your walls are cool, will humidity condense on them in the summer?
Radon is normally vented with a pvc pipe (4 inch?) that runs from below the basement slab out through the roof. The polyethylene vapor barrier should be below the slab and above 6 inches of compacted gravel. The air spaces in the gravel allow for radon to reach the vent, (and also reduce the amount of ground water that wicks up from below). You can use landscaping fabric below the gravel to prevent it from getting filled with mud over time. To prevent the concrete from settling, borrow a vibrating compactor to use on the earth before laying the gravel, then again on the gravel. As for cost, where I live gravel is almost as cheap as dirt, and is hauled by the same companies.
I think you can do the concrete slab yourself, in batches. Just plan on having some kind of pattern to accommodate many smaller pours. You could do a 4” slab, if you keep the wire mesh in the center and have a joints less than 16 feet apart, and if your concrete isn’t junk.
When you are done, test for radon. If it is high, add an electric fan to the radon vent.
Oh, and, get a building permit if it's required.