-(은/는) 것은 바로 그 때문이다 vs -기 때문이다
I learned the following two expressions:

제가 가고 싶은 것은 바로 그 때문이에요.
That is why I want to go.

제가 가고 싶기 때문이에요.
It is because I want to go.

The two English sentences have different meanings, but I may be translating them incorrectly into Korean.

1) Do the Korean sentences actually have slightly different meanings? If so, how?

2) Can I use the following more naturally in conversation? 그래서 가고 싶어요. (Therefore, I want to go)

감사합니다!

Question

-(은/는) 것은 바로 그 때문이다 vs -기 때문이다
I learned the following two expressions:

제가 가고 싶은 것은 바로 그 때문이에요.
That is why I want to go.

제가 가고 싶기 때문이에요.
It is because I want to go.

The two English sentences have different meanings, but I may be translating them incorrectly into Korean.

1) Do the Korean sentences actually have slightly different meanings? If so, how?

2) Can I use the following more naturally in conversation? 그래서 가고 싶어요. (Therefore, I want to go)

감사합니다!

Answer

"제가 가고 싶은 것은 (바로)그러한 이유 때문이에요." is more natural. /
"제가 가고 싶기 때문이에요." is correct. /
"그래서 가고 싶어요." is also correct. /
As you said, two sentences have different meanings. There could be some reason in the first sentence, but there could be no reason in the second sentence. The other example is "특별한 이유는 없지만, 제가 그냥 가고 싶어요."