Despite their agreement that the female voice is not `awra, several of the answers indicate that listening to a female singing, regardless of the level of excitement incurred, is disliked or forbidden.
For example, Shaikh Amjad, whose fatwa you linked to, says, “As for singing, scholars stated that hearing the singing of a woman is offensive, unless it fitna is feared from it, in which case it becomes unlawful.” And Shaikh Faraz concurs, “It is not permitted for men to listen to the singing or recitation of strange (non-mahram) women, whether it is with or without the fear of fitna.” I can’t find a fatwa that diverges from this opinion on the site, w’Allahu a`lam. Perhaps its an issue that the scholars disagreed about; I don’t know.

Jazak Allahu khairan.

Link 1: http://qa.sunnipath.com/issue_view.asp?HD=3&ID=3768&CATE=368
Link 2: http://qa.sunnipath.com/issue_view.asp?HD=1&ID=1361&CATE=88

SunniPath is a very diverse site and on that subject there are numerous opinons on different subjects. On the subject of the voice of a woman being Awrah, the answer seems to be unanimous.

http://qa.sunnipath.com/issue_view.asp?HD=1&ID=1786&CATE=142

“Any singing that is accompanied by other sins, such as songs that consist of unlawful, immoral, and sexual themes, or it is sang by non-Mahram women, etc will also be unlawful. This ruling is also with the consensus of all the scholars.”

wa salam alaikum!

as-salamu’alaikum,

No the woman’s voice is not considered Awrah (see: http://qa.sunnipath.com/issue_view.asp?HD=3&ID=4835&CATE=368)

But there is a matter of what is best and proper according to the circumstance, and judgement. If there is fear of fitnah in your listening to this Qasidat al Burdah, in that you have become sexually excited, then yes indeed it becomes awrah for you and its best you don’t hit the play button. Though, there are probably quite a few things that you would need to avoid in life as well.