I've done back-sweetened, carbonated non-beer things in the past. Basically, what Richard suggests is the way I do it:
after fermentation, stabilize to kill yeast; add a small amount of sweetner (preferably dextrose disolved in boiled, cooled water) to keg; stir, sample; add more to taste;
then force carb to about 3.5 volumes.
As for the left over, I'd just pop that in another keg!