I used it to do my collimation however, my eye pieces do NOT fit snugly, and require a setscrew to hold them in which of course "presses" the eyepiece off center against one side of the focuser.
The diffraction-limited field of your scope may be small, it's not
that small.
I know that if I use a laser (tightened in place with the set screw)the laser beam is definitely off to one side of center and if I "center" that, then the collimation cap is shows the collimation to be off to one side.
You're not using the tools for which they're good. I'll assume, for the sake of the argument, that the laser collimator is itself collimated (if you rotate it in the focuser and retighten it, does the laser spot on the primary move?).
The laser collimator is good for pointing the reflected focuser axis at the primary's centre (by changing the tilt of the secondary).
The collimation cap (placed close to the focal plane) is good for making the reflected optical axis cross the focuser axis at the focal plane (by setting the tilt of the primary).
Given that they essentially serve two different purposes, they can't "disagree".
By the way, the return beam of a laser can be used to set the tilt of the primary *roughly*, but it's much less precise than the mundane collimation cap for doing so, because the return beam is only precise if the forward beam hits the primary's centre perfectly -- much more perfectly than is necessary for pointing the reflected focuser axis accurately enough.
To answer you last question: well, if the focuser draw tube is wide enough to make eyepieces "rattle", there is not really such a thing as a stable focuser or eyepiece axis, so part of the collimation becomes a fuzzy concept at best (even though the most important thing to do, i.e. make the optical and focuser axes cross at the focal plane, is still achievable for a given position of the focuser, pointing the focuser axis to the primary with a laser collimator becomes well nigh impossible). The end result can be a tilted focal plane (troublesome at low powers) or collimation that can only be good for one focuser position (if the eyepiece axis isn't parallel to the focuser travel axis, different eyepieces "want" a different tilt of the primary depending on where their focal plane lies in the eyepiece barrel).
Frequently, the fault lies not in the focuser but in the poor quality of the 2"-1.25" adapter (assuming you have 1.25" tools and are talking about 1.25" eyepieces); getting a better one may already help.
Finally this: collimation tolerances on an f/6 scope are rather generous, so do the best you can and enjoy the view while you're figuring out a way to chase the mechanical gremlins.