First, he didn't rely on the given words as much as he did on his first attempt.

What you wrote is perfectly fine.

But I have a suggestion.
It would sound better not to use "First" twice here, and also, the first "First" suggests that there will be a second point later. There is a second point later, but it is not introduced as a "second" point, so it lacks the symmetry we often use when we write something such as

First, he did something somehow somewhere.
Second, he did another thing somewhere else.

You can also use "Firstly" and "Secondly" as a pair like this, and if you use "Firstly" here, then you don't have the word "first" repeated.

Or you could use "First of all" and "Secondly" as a pair.

He sounded more natural and clear too.

What you wrote is perfectly fine.

But I might say

He sounded more natural and also more clear.

I don't know why, but I like the sound of it better this way.

And the morest noticeable improvement, in my opinion, was in the way he had organized his ideas.