This issue is not likely to be resolved any time soon but it does provide for an interesting discussion. I was thinking about your argument that aliens are subject to the presiding courts but, doesn't the term "subject to the jurisdiction thereof" refer not just to the courts but to the United States as a nation and the states as a sovereign entity.
The reason I mention this is that I can think of several obligation imposed by both the United States and the various states on citizens subject to full jurisdiction that are not imposed on illegal aliens or casual visitors. Included in these obligation are registration for the military draft, reporting income earned outside the United States, presenting a passport prior to traveling outside the United States, serving on juries, both state and federal, obtaining a social security number prior to a given age, compulsory education and several others. In addition there are the matters prohibited to illegal aliens and visitors such as voting, holding elective office, serving in certain professions and several others.
My point is that jurisdiction as expressed in the 14th amendment does not seem to be confined to relationship to the judiciary. Citizenship is full lifetime membership in a nation. Members can pass that blessing on to their children without restriction but the membership reserves the right, through their congress, to determine who and how many others to admit to membership.