I don't know much about the 08+ SJ's. If you got the top and bottom decks for $2k and had to assemble them that would be cool. Finding all the stock parts for $1k is going to be tough though... Maybe $2k if you're buying parts individually. I spent $2k on my ski over the winter just building it up and I had just about everything already including a b pipe.
Expect a decent 61x engine with carbs and flywheel only to run $500 or so. You've still got to get a pump/prop, rideplate, intake grate, pole, hood, pipe (don't even bother with the stock pipe), fuel tank, all the cables, waterbox, midshaft, steering, switches, etc... It'd be easier and cheaper to find a donor ski and sell what you don't need.