Your theories about the siddurim of the GRA and Baal Hatanya are reductionist. Actually, both were extremely well versed in kabbalah, and they worked on their siddurim to be consistent with what they felt was proper according to their kabbalah. The ex post facto does not apply to them. Neither followed popular or customary practice to determine what was the premier nusach. As I noted above, there were nuschaos that became widespread that were actually forgeries that somehow got included in prevailing nusach. Since these were inconsistent with kabbalah, they were filtered out.
One additional note – the Siddur HaGRA has been published numerous times, firstly titled Ishei Yisroel, later other labels used. In many cases, until recently, the nusach was not 100% accurate in the text of the siddur, and one needed to resort to other sources to be more precise about the actual nusach of the GRA. Supposedly, those areas of mistake have been corrected in the most recent editions.