Does salt-seasoned pasta and starchy water in my sauce have to yield a salty sauce?
Since cooking the pasta in salted water is essential, and switching to fresh water or whatever is a PITA, I'd just use less water and thicken with something else. 

The standard ratio for salting pasta water is 1:10:100 - 1 litre of water for 10g salt and 100g pasta - perhaps you're over-salting the water?