Philosophy doctorate and prof here. Excellent game!!!! It's great to have everything broken down to its basic parts like this. Looking forward to a sequel! (is asking to debate Wittgenstein too much?) The logic in terms of where to put the objections actually holds up really well (you've clearly done well in symbolic logic; something a good number of commenters who question the placement of the gameplay mechanics probably never took), which is usually not the case in the ace attorney series.
*spoilers* It was rather predictable that the final answer is a consequentialist answer, using utilitarian assumptions (which you had already poked some appropriate holes in previously). It kind of spoils the intended ending by de facto endorsement of both the Arbiter and the game creator of utilitarianism that its central premise of happiness = good remains unchallenged throughout the game.