Level has no bearing on chuck runout. You need to preload the jaws from the outside, something that can be tricky. There are some clever ways to do it, but they require machining certain tooling aids. If this is a 2 piece jaw chuck (bolt on top jaws and fixed master jaws0, you can use a piece of plate and drill 3 holes @ 120° at the proper place and using longer than standard bolts, afix it to the top of the removable jaws, then tighten the chuck against that. It's a lot of work, but mimics the forces usually seen when chucking a piece of material. That's the key. Think of how the forces play out when you have a piece of material in the chuck.
Another thing that people do is simply put a short piece of bar at the very back of the jaws, and tighten the chuck on it. Of course, this will cause the jaws to close more on the front, because there is no support from any material. Then they grind as far back as they can without crashing into the short bar. When they finish grinding the jaws, they remove that short bar and just leave the chuck loose and grind the short area where the bar was larger than the front area where they ground with the bar in the chuck. Naturally, and especially on an older chuck with wear on the jaw slots, this will cause a bit of bell mouth on the chuck. So it isn't really a great way to do it. If you can outguess that taper and grind accordingly, you can end up with usable jaws though.
Also beware that on on older chuck, if you do grind the jaws, and they come out running true, wear on the scroll may cause the runout to be even worse in positions other than where you ground the jaws. Like different sizes of test bar. May be fine on a 1" but horrible on a 3/4", or just the opposite.
Just a couple of things to think about. There are a few threads here showing how some of our members managed to improve their chucks. A search should bring them up, or some of those members will chime in on this thread.