Good question.
In my opinion, (and I am open to change my mind if presented with good hermeneutics) I think it means what most think when they read it without any explanation.
But Moses said to the LORD, “Oh, my Lord, I am not eloquent, either in the past or since you have spoken to your servant, but I am slow of speech and of tongue.”
The thought that comes to most people is that he was having a problem with articulation. Slow to speak or find the right words in the language he would need to speak to Pharaoah. He did not think he was eloguent. That means he did not think he had the mastery of the language that would make him appear to be a "well educated, and articulate speaker."
Now Acts says 7:
21 ...and when he was exposed, Pharaoh’s daughter adopted him and brought him up as her own son.
22And Moses was instructed in all the wisdom of the Egyptians, and he was mighty in his words and deeds.
But now he had lived 40 years having to speak a different language. He felt like he had lost the mastery of the language of Pharoah that he once had and it would be obvious to Pharoah and everyone. He felt he would be struggling to remember words and faltering in his delivery. And he was right. God did not care, God did not give him supernatural recall so that he suddenly was as fluent as he once was. He says... " since you started telling me to go do this I have not experienced a change in my ability to remember that language as I would need to in order to sound impressive to Pharoah. They are going to think I am not very smart when I am taking a long time to remember each word to say."
That is the spirit behind these concise words that I get from a natural reading of the text. I never understood it as saying that Moses stuttered or had a handicap.
Before he killed the Egyptian and had to flee he was Mighty in his words, and in all the wisdom of the Egyptians. It was probably his having grown forgetful of the command of the language that he once had that made him so self conscience.
But you are right. It is one of those things that will never be answered. There is no way for me to prove my theory. There is no way for any scholar to prove he had a stutter. The Hebrew does not say that. The Hebrew means the same as the English translation in this case. We can all speculate but the best translation in this case seems to be Moses own lack of confidence in how he would come across. I believe he got over this after he returned and started conversing with the people again and his learning curve, recovering his old mastery of the language went well and he once again was mighty in words, in the language that Pharaoh could understand. It does not look like he needed Aaron to speak for him much after things started moving forward in Egypt.