Which is fine and I'm not challenging your statements on Islamic jurisprudence - all I'm saying is that it's not relevant to the situation at the time of Ain Jalut, forty years previously. At the time of Ain Jalut, Berke was angry with Hulagu because of his treatment of Baghdad and the Caliph and was aiding the Marmeluks indirectly against Hulagu forces. Later Berke fought a war against Hulagu where religion was one of the factors.
If the Marmaluks had been eliminated (as they were later eliminated by the Ottomans) then the likelihood is that the Levant would have been devastated much as Baghdad was. Without the distraction of the Marmeluk front Hulagu and his sons may be much more successful against Berke which may butterfly the need for the Ilkhanate ever to formally adopt Islam (with or without the fatwa). You may have a situation with a residual Crusader presence in the Levant and a much stronger Christian presence (and corresponding weaker Muslim presence).
Of course. Now let us get back on topic haha.