As you have already checked the inside of the spindle for runout, which seems, within your measuring capabilities, as OK, then really the things to suspect are the bits you are wacking up into it.
You should find it much easier to check for runout of tooling using your lathe, and I think as yours has a morse taper spindle, it is easy to stick the bits what you want to check into that.
Unless you have made the tooling and arbors yourself, and you know they are right, then don't trust cheap tooling at all, always check and put things right before using.
I have been very lucky with my keyless drill chucks and arbors from RDG, both R8 & MT3, I have about a dozen of them, and none have any detectable runout. As for ER collet chucks, mine is a very early one, and runs perfectly true, but I have had to true up a couple of new ones for people that have had runout as much as 0.004" (0.1mm). That figure must be less than 0.001" (0.02mm) or even better, none at all, otherwise, they are not worth using.
They don't have to be ground, if you are very careful, they can usually be trued up with a normal cutting tool and using the topslide set up exactly to the correct angle.
I've done a post somewhere showing how I cut the taper for an ER collet chuck, the same method could be used for truing.
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