If the reason why you are saying that it’s okay to eat the rice in Case 2 (and possibly in Case 3) is that he had in mind when he made the Al Hamichya that he wants to eat rice, wouldn’t that be the same as someone who made an al hamichya but had in mind that he wants to continue eating cake?
In the case of someone who made an al hamichya and had in mind that he wants to continue eating cake, I’m think the halacha is that you are not allowed to continue eating cake. I think that I read in a halacha sefer that it’s a machlokes and therefore you are not allowed to continue eating the cake since we are choshesh for both opinions. That also seemed to be what the biur halacha you quoted (Siman 190) was saying as well.
Or do you see a difference between the 2 cases?