この仕事が無事に＿ ＿ ⊛ ＿、心から感謝している。

Question

After reviewing some old 新完全マスター material I came across this sentence, which took me a bit to parse:

この仕事が無事に＿ ＿ ⊛ ＿、心から感謝している。

1. チームワークが
2. 終わるのは
3. ほかならず
4. よかったからに

My "immersion reflexes" kicked in and I selected 2-1-4-3. I got it right, but the solutions manual just provides the correct answer (not the actual order).

My thought process is the following: First of all the only thing that can fill the first gap is 終わるのは (無事に終わるのは has such a natural flow). Also, 3 must follow 4 since 4 ends in に, thus completing the pattern にほかならない・ならず. Putting it all together 1 has to fit the 2nd spot (since putting it on spot 4 is completely invalid), thus getting the final sentence:

この仕事が無事に終わるのはチームワークがよかったからにほかならず、心から感謝している。

which roughly translates to something like:

This job was completed successfully only because of good teamwork, for which I am sincerely grateful.

Since I couldn't confirm this anywhere, I wanted a second opinion.

If it is indeed correct, let this work as a reference for the next person who might be wondering the same thing.

Answer 1

Perhaps you've missed the cleft sentence grammar? This is a combination of the following two patterns:

• A(だ)からB ⟶ BのはA(だ)からだ ("It's because (of) A that B")
  _{(A cleft sentence where the reason part (から) has been pulled out for emphasis. See this)}
• Aだ ("is A") ⟶ Aにほかならない ("is nothing but A")

Putting the two together, we get:

• BのはA(だ)からにほかならない ("It's exactly because (of) A that B")

Thus a literal translation is:

この仕事が無事に終わるのはチームワークがよかったからにほかならず、心から感謝している。
It's exactly because our teamwork was good that this job was completed successfully, (so) I'm sincerely grateful.

Your translation attempt is correct, too.