Is it permissible for the Commander of the Faithful to impose his jurisprudential school of thought upon the subjects, and be obeyed in that for the sake of unifying the word of the Muslims, by analogy with some Companions praying behind Uthman, completing the prayer despite their view that it should be shortened?

The Commander of the Faithful is not permitted to impose a specific jurisprudential school of thought (madhhab) upon the subjects, because the wisdom behind the اختلاف العلماء (disagreement among scholars) is clear. There is no madhhab or Imam who was correct in all of his sayings. Had Allah willed that there be no disagreement, He would have been capable of that. The Companions completing their prayers behind Uthman in Mina was due to the general meaning of the Prophet's (peace be upon him) saying: "Indeed, the Imam was appointed to be followed, so do not differ with him." If the Imam wishes to impose a single madhhab, then obedience to him in that matter is not obligatory, because obedience is only obligatory in what is good and permissible (ma'ruf), and this is not among it.