3C collets. I check the runout from the collet socket on the mill spindle and see ~.002. Insert the collet and see about the same at the base of the collet, but ~.012 about and inch away from the base. Also the draw bar I have is pretty tight within the spindle barrel, so I'm looking to eliminate one variable to see if I get improvement.
Some thoughts for you...
I agree the draw tube should be setting the straightness. However, 0.002" run out of your spindle also seems unreasonable. Something is wrong here and working on the collet or draw bar would not seem to solve this issue. However, you say the run out is far worse about 1" from the collet base. (What do you mean by "base"? The bottom edge of the gripping surface?) Put a good cylinder, as though it was an end mill cutter, in the collet and measure the run out along the cylinder as a function of distance from the clamp end of the collet. This will tell you if the collet gripping surface truly is not parallel to the spindle axis. Even a decent drill rod will have a better surface and roundness than 0.012". So you could insert it and measure runout along several inches of the rod. Then there is also the issue of having debris stuck inside the collet which would tilt the end mill or drill rod.
By the way, we know that one cannot match all of a surface at one time. Two surfaces contact only at three points only (provided the two objects are perfectly ridged planes). These three points define the plane (parallelism) of operation. When the rest of the surface is very close it provides strength as the metals are deflected (not perfectly ridged) and the contact points change or broadened. Think of this as you would scraping a surface or a mating way. Only the high points contact. Only, in the case of a way, where things are sliding as wear occurs the high points actually wear down and the point contact surface area increases somewhat.
If the spindle is actually true and the collets are good then it would seem that there might be something wrong up inside the draw tube. Perhaps a rough spot or debris is stuck inside pushing one end of the collet off center. I would think that you might be able to feel something that causes 0.012" run out. Look up in the draw tube or at lease run your finger around the inside. Is this run out true for all of the collets or just one? If so maybe the collet is bad and does not seat properly.
One other thought. My spindle/draw tube, as well as the collet, has a pin/shear pin and groove system to lock the phase of things and keep them from rotating as they are being tightened down. I damaged this shear pin once when I had a crash and so I had to disassemble things and remove it . I found that it had probably been partly sheared off before and so this sheared debris might have been tilting the draw tube as material could have been wedged at the draw tube mating surface. Hence it would have caused runout.
(IF you could measure the phase of the run out.... Is it constant relative to the spindle rotation? In the UNLIKELY case that the collet does not have a locking pin, then rotate the collet some amount (45 degrees) before clamping it and measure the run out and PHASE again. If the collet is bad would the phase of the runout not rotate with the collet? If the draw tube is bad wouldn't the phase remain the same as it is locked to the spindle? If the phase is all over the place would that not imply that the spindle has random bearing errors? There are probably other possible issues or causes that might be observed?)