You have to know what to expect from a chuck. You are probably "swallowing" the work - seating it all the way in to the body. Not a good thing to do. All 4 jaw chucks have to be treated as though their jaws were slightly sprung. Very few have the gripping surfaces precision ground in place. Therefore there is no guarantee a 4 jaw independent chuck will grip straight. Neither do three jaw universal chucks once they've been in a few small wrecks but that's another subject.
Swalllowing the work is poor practice bexasure you can't bumber the uverhang into concentricity. Even if you do the slight wirks in the grip while the cuts are in progress causes the grip to drift back to the original orientation.
The solution to dialing in finished work in a 4 jaw chuck is to grip only a little of it or grip it in a short ring of copper. Make sure the ring of copper is in the plane of rotation. If it is not the gripping force will make it impossible to dil in the wobbling far end.
I wrote a couple of tutorial articles for the 3 jaw and 4 jaw chuck. Send me your email and I'll send the .doc files to you.
I've dialed in long high-precision work in a lathe to 0.0003" in a worn out 4 jaw chuck in a 36" lathe using the copper ring trick (Is the spindle sleeve for a 340T G&L horizontal boring mill precise enough for you?) Padding chuck jaws to protect the work and to aid dialing in the far end is technique old as the metalworking lathe.
OK, once you have gripped the precision work in a copper ring and you have ensured the ring lies in a radial plane, dial the work in close the the jaws. Then move out a ways and bump the far end of the work into concentricity being careful not to jar the indicator or its delicate guts. Use a lead or copper hammer or maybe wood or hard plastic. Soft face rubber or plastic hammers are too soft. They lack the essential shock needed to nudge the work in tiny increments.
Adding: My version of a "copper ring" is an incomplete circle of annealed #6 bare copper wire snipped from a longer piece I keep handy by the lathe. So long as you get copper under all four of the jaws all is well. The jaws of my chuck are serrated. #6 copper wire happens to fit the serrations. YMMV
You guys with smooth chuck jaws may benefit from a piece of copper pipe or a 3/8" wide strip rolled to approximate diameter. Lead is too soft, Plastic will crush or simply squirt out, aluminum is a little slippery. Soft iron works OK for hard work but will indent unheat treated steel and most all non ferrous metals. Paper is too thin, cereal box cardboard works OK but you might need a couple of layers. Gasket material is hard to beat for some applications but it has to be 1/16" or the jaw serrations will punch right through it.
Go back and forth dialing in close to the chuck and tapping in the far end. You will find that a little practice leads you to dialing in precision work to 0.001" TIR or better if you wish. When I was an apprentice we had to go against the clock. If we could dial in a hunk of 4" stock bother ends within two minutes we got that box checked off. Most of us got it with time to spare.
The next thing to address is security of the grip. One might think gripping work in a narrow band of coppr is precarious or even dangerous. There's truth in that so you have to proced with due caution. That's why you use a steady rest or a center once the work is dialed in.
This is part of lathe work. You cannot always depend on a sure immovable grip. The pressure of the jaws may force thin-walled work out of round. You may have to face off the end of a long part that cannot be supported and center drill it. You may have to face work parallel and there is no way to access the back side for dialing in except between the jaws. There's dozens of seemingly impossible-to-solve lathe problems. There are solutions to all of them. Time and experience will bring the answers to you. Many you will solve for yourself. The others us decrepit old timers will help you. Have fun with both alternatives.