I take it that you are measuring runout rather than spindle to ways misalignment. You are correct as to the possible sources. Any or all three could be the cause. Parsing them out is where the difficulty arises. I think the suggestion to use dowel pins id a good one. They will have a tighter tolerance than drill rod. Be aware though that even dowel pins do not have a specification regarding straightness (cylindricity). I personally like wrist pins from internal combustion engines. They are generally very straight and have good roundness and diameter specs. I have a collection ranging from 7/16" to 1-1/8".
You can determine if straightness of your test pin is at play by marking the spindle on its side and measuring the runout. Mark the pin on its side at the point of maximum or minimum runout. Then rotate the pin 180º, being careful not to allow other components to rotate and remeasure runout. If the runout moves with the pin, the pin is out of round. If it stays with the spindle, another component is at fault. You can use this procedure to check the collet and the collet chuck as well. Be aware that runout will stack up and it is entirely conceivable that it can be in a way that the various runouts can partially or entirely cancel.
A 5C collet, properly used will grasp a pin along the entirety of its ground length. As the collet is tightened. the flexing portion will bend in an S shape so that the inner and outer surface surfaces are coaxial. The amount of force required increases greatly as the difference between the diameter of the pin and the the design diameter of the collet increases. At some point, it will be too great for a collet closer to work. One reason for the smaller grip range of 5C collets. Any pin which is smaller in diameter than the collet diameter will only grasp on three lines spaced 120º apart.
ER collets and other double angle collets require less force to deform to fit, hence the larger grip range. They also have four, six, or eight fingers as opposed to the three of a 5C collet. The double angle feature does add another surface which can deviate from the ideal and the nut threads of an
ER collet chuck adds one more. Sorting it all out can be time consuming and oftentimes frustrating.I believe in the philosophy that in the practice of machining, there is no such thing as a perfect part. Everything made will have some variation. It may be too small to measure but it is there. When these variances stack ip, we can begin to see them. If there is an angular deviation in grinfing the surface of a collet, it may only measure a half thou close to the face of the collet but it may be ten times that 5" out.