Tomoy, sounds like you are doing a good job analyzing the possibilities, so I'm not sure I have much to offer in that regard, but I do have similar problems. I notice it most when I am skating and sharing a lane with someone else. Even if I am going straight forward, my feet have a tendency to kick the lane line, which is a sure sign of alignment problems. In my case, I think it has to do with a lousy right shoulder, and I believe I can correct most, if not all, of this problem by spearing deeper with the right arm and focussing on keeping that right arm aligned on a straight track while I kick. Sometimes I have a tendency to try to lift the arm too high, which my shoulder won't allow. So in order to get the arm up, I mess up my whole body alignment.
Of course, I may be doing the same thing in full stroke and not noticing it, or not knowing what the cause is. Skating can tell you things about your full stroke, but only if you listen and try to draw the consequences.