Din 

Reason 

Rabbi Eliezer 

One can only eat until the time of Biur of the very first type 

Because even the last type contains a forbidden taste of the first type. 

Rabbi Yehoshua 

One may eat until the time of Biur for the last type has come 

Because even the first contains permitted taste from the last type. 

Rabban Gamliel 

One may eat each type until the time of Biur for that type. 

Because taste doesn’t matter in this context. 

These explanations are from the Meiri. It is not clear why having permitted taste would permit other types according to Rabi Yehoshua, nor why taste wouldn’t matter in this context.