I don't see where you get the nuance of more. There isn't any at all in the context of the Korean sentence.
You are correct. However, "more" can also have different nuances. If we start the sentence with 이제 you might make a case for "Now there is no more furniture in the living room." with the meaning the furniture is totally gone. However, I think your "at all" is the most representative of the normal Korean intention. 도 is being used to emphasize the fact there is no furniture, probably because it is an unexpected situation. The DL translation is poorly chosen and doesn't reflect the usage of 아무 가구도, and would be used as a translation for "거실에 가구가 없어요."
Correct, but better still would be to add "at all", "whatsoever" or insert "absolutely" in front of no. If you want to get really creative and are notching your belt with accepted corrections, try" The living room is totally without furniture."