Is it possible that all the affordable project cars are now taken?

You may not be looking into the right places.

Granted the days of 500 dollar Mopars are mostly gone, you can still get project cars under 3k if you look around. Sometimes running, some times not.
I’m in a new area so all I have is marketplace/Craigslist and word of mouth. But I’m keeping my eyes open to all the farms around me for treasure.