word choice - The differences between "To" and "So that" in an "instrumental" function. When is one not interchangeable for the other?

I'm trying to think about "to" and "so that" when describing means and purposes and have come across this following problem.

I feel like the following sentence is pretty natural.

"You have to try hard to succeed."

Means: Try hard.
Result: Succeed.

But although the following sentence adheres to the same structure and usage, it feels quite odd.

"I'm trying to do all my work now to go home early."

Means: Do all the work now.
Result: Go home early.

When I ask friends if this sounds natural to them, they all unknowingly convert the sentence to...

"I'm trying to do all my work now so that I can go home early."

Means: Do all the work now.
Result: Go home early.

On the other hand, using "to" feels much more natural in this sentence, which I feel is similar to the previous problematic sentence:

"I can't believe you spent so much money to impress that girl."

Means: Spending a lot of money.
Result: Impressing that girl

My questions are:

1. Is that sentence which I feel to be odd grammatically acceptable?


2. Why is it that "so that" so naturally replaces to in the sentence?


3. Why does "to" feel more natural in the final sentence, whereas it felt odd in the previous sentence?

Answers to even one of these questions are appreciated.