On the one hand this can come to mean that the fault is with Moses (that he may even have a physical disability that limits him in his role as a communicator).
Alternatively, the descriptor of his lips is based on an internalised narrative created by the reception he gets from his audience. Just like the spies in the desert that said "we are as small as grasshoppers" - they were not in fact the size of grasshoppers, instead they felt like they were based on their encounter with other.
Similarly, the commentator Sfas Emes points out that Moses describes himself in this fashion because the people refused to listen to him. So if they cannot hear, then perhaps it is because he cannot speak. The Sfas Emes goes on to say that prophets are made by the community (Ps50:7) that is willing to heed the message of the prophet otherwise they are just a person screaming into the wind.
(7) “Listen, My people, and I will speak, O Israel, and I will arraign you. I am God, your God.
(10) But Moses said to the LORD, “Please, O Lord, I have never been a man of words, either in times past or now that You have spoken to Your servant; I am slow of speech and slow of tongue.” (11) And the LORD said to him, “Who gives man speech? Who makes him dumb or deaf, seeing or blind? Is it not I, the LORD? (12) Now go, and I will be with you as you speak and will instruct you what to say.” (13) But he said, “Please, O Lord, make someone else Your agent.” (14) The LORD became angry with Moses, and He said, “There is your brother Aaron the Levite. He, I know, speaks readily. Even now he is setting out to meet you, and he will be happy to see you.
The Midrash continues that Aaron is an altruistic leader and is happy to follow in the footsteps of his younger brother. This altruism is the quality that enables his descendants to be the cohanim... to be the priests serving God in the tabernacle and in the future Temple in Jerusalem instead Moses' descendants. This demotion comes as a result of God declaring his anger at Moses' refusal to lead the people. This is the first time in the Torah that God is described as angry.
Perhaps this angry punishment is for a higher purpose, maybe it is a test for the brothers? The midrash imagines that they pass the test as Moses congratulates his brother for his new lofty role and Aaron bemoans his younger brothers inability to serve in an ongoing role and one of such close proximity to God. They truly are the vanguard of a new brotherly and prophetic paradigm.
(23) A long time after that, the king of Egypt died. The Israelites were groaning under the bondage and cried out; and their cry for help from the bondage rose up to God.
However, the verse from Exodus points out that Pharaoh had died. So many commentators read that sentence as a metaphor.. he did not actual die in body but it as though he did die but instead just became severely ill with leprosy.
This helps maintain the symmetry of the Pharaoh that ordered for babies to be thrown in the Nile to have his own son killed. Otherwise, the literary symmetry breaks with it being Moses' brother who never ordered the death of Israelite boys - but did perpetuate the slavery of the people.
By the hand of some other person whom You choose to send — for in the end “I” shall not bring them into the land of Israel nor shall “I” become their deliverer in the future — and You have many messengers! (Pirkei DeRabbi Eliezer 40)

