1/4 turn is excessive.
Three ways to get rid of slack in the throttle cable, and none have to do with the rise of your bars. The slack is function of the length of the cable versus the cable housing, not the height of your bars. First, where the throttle cable threads into the throttle housing, you should be able to lossen it back a few turns (especially if you screwed it all the way in). Once you've done that, there is a nut that you can tighten so that it doesn't move anymore. Second, at the end of the bend at the top of the cable (the metal tube part), there is another place to adjust, with a nut and a long adjustment nut. Back out the long one, and use the regular nut to tighten up against that. Third, where the cable mounts to the carb, there should be a threaded and one or two nuts, and you can adjust it there. It will all make sense if you look at it for a second.