You can get some movement in the indicator reading by just turning the chuck by hand, I use my VFD jog which is 6Hz, this is slow enough and I run the indicator along the bar while turning. Also try to put the gearbox in neutral as opposed to in gear if turning by hand. The dial indicator head I use has a flat convex head, so more contact area, if your dial indicator is off from vertical then you can easily see a variance of 0.001". At 10-12" on a test bar I will usually see a swing of under +/-0.001", you are getting quite a bit more. The problem with most 4J independent chucks are the jaws have very course serrations so it may not clamp evenly, my 4J jaws are 0.200" at the tips with no serrations. You might try to repeat the test with a 3J, you are not concerned about the TIR, just the swing around "0" remains the same magnitude in either direction. This tells you if the head is aligned relative to the carriage position. Beyond that the two ring test can be used to further fine tune/check the alignment while cutting, this is also true of the tailstock once the head is aligned. Many of the newer dial indicator use the name of some well known prior manufacturer, but the internals are often lacking. My go to dial indicators are the Starrett 25-511 or 25-611, they will read 0.0001" and have a range of 0.200". NOS are lightly used ones come up at auction in the $60-100 range, super nice to work with and very accurate.