Is the Rabbi’s criticism directed at the comparison to “anything that does not take effect one after the other,” or at the Maharal’s underlying reasoning itself?

If we assume that specifically a broken piece is “bread of affliction” and a whole one is not,
and if we assume that if one eats a whole piece and afterward a broken piece, then he also has not eaten “bread of affliction,” because he already ate matzah that is not of affliction,
then the Maharal says: if so, then eating a broken piece together with a whole one also should not count as eating “bread of affliction”; an eating in which he has a whole piece in his mouth is no more “afflicted” than if he had already eaten the whole one beforehand.
And therefore he explains it differently.

This has nothing to do with “anything that does not take effect one after the other.” When the problem is precisely that it comes afterward, why shouldn’t doing it simultaneously help? Take as an example: one prohibition cannot take effect on top of another prohibition. One after the other it does not take effect, but simultaneously it does.
“Anything that does not take effect one after the other” is said in a situation where one interferes with the other by its very nature, like betrothing two sisters. But here one does not interfere with the other; rather, if he did the first one, he has already fulfilled his obligation.
As for your reasoning that in practice he ate, it seems to me that that is דווקא not necessarily compelling. He is not talking about the ability to eat, but about the ability to fulfill both commandments. His claim is that even if he ate both of them, it is not certain that he fulfilled both commandments, because they do not apply one after the other.

Let’s leave aside the comparison to “anything that does not take effect one after the other” and deal with the Maharal’s actual reasoning.
The issue is not fulfillment of obligation but eating “bread of affliction.” Eating bread of affliction is only the first eating of broken matzah. Eating whole matzah, or eating broken matzah after one has already eaten whole matzah, is not eating bread of affliction. The way of a poor person is with a broken piece, because he does not have a whole matzah. And about this the Maharal says: “Since if he were to eat from the whole one and afterward from the broken one, he would not be fulfilling ‘bread of affliction’ with the broken one, then when he eats them simultaneously as well, it is of no effect at all, for he is also eating from the whole one.” Does it make sense to you that eating a broken piece and a whole one together is eating bread of affliction, but eating a broken piece after he already ate a whole one is not eating bread of affliction?

I assume that from his perspective, “bread of affliction” is a defining condition of the commandment, and when you ate half a matzah you ate bread of affliction—even if along with it you also ate other bread that is not affliction-bread. But one after the other, there is no bread of affliction here at all, because the first one is the matzah-eating that fulfills the commandment.