You wrote in your Point by Point summary:
"i. However, if only the end is considered Shechitah, at the start of Shechitah (i.e. after cutting more than half the Kaneh, or any amount of the Veshet), it became unusable for Pesach (Sheni, since it will not live until then)."
I don't think that the point is that it will die--since there is also an opinion that a Tereifah may live -- but rather, I think, that after the partial Shechitah made the animal a Tereifah, it is a Ba'al Mum.
Even though the Chatam Sofer says that a Mum Over might still heal and be kosher by Pesach Sheni, a Tereifus certainly cannot heal and therefore I assume that it would be pasul as a Ba'al Mum.
Rabbi Zecharia Dor-shav, Yerushalayim
I think that the case of Kaneh and Veshet may be different, because Rava concludes later (32b) that if there is a hole in the Veshet, or the Kaneh is cut, this is a Neveilah (see Rashi there, DH v'Yesh). Even according to the opinion later (42a) that a Tereifah can live for 12 months, in the cases of Nekuvas ha'Veshet and Pesukas ha'Kaneh he will agree that it cannot live because it is a Neveilah. See Rambam (Hilchos Shechitah 3:19), who writes that if the majority of the Kaneh is cut or there is any amount of a hole in the Veshet, the animal is a Neveilah even if it is still alive.
Kol Tuv,
Dovid Bloom
The point that I am making is that even before Rov Kaneh has been cut--and it is only a mum over--it is already not fit for pesach sheni, because you can't bring such an animal to the Bet Hamikdash and have it accepted. Therefore, before it became a neveilah--if he stopped cutting the neck before it was rov and waited for Pesach sheni--it would be pasul.
As regards the veshet, see the Tosefot Harosh on 32b, who argues that a puncture of the Veshet does not make an animal into a Neveilah.
Zecharia Dor-Shav, Yerushlayaim
Dear Rabbi Dor-Shav, thank you for your important and incisive comments.
1. In Daf Outline, and in my answer, we related to the scenario where the majority of the Kaneh was cut. I would agree that if only the minority was cut, it would be a Mum Over. (I would add, however, that according to Raban Shimon ben Gamliel in the Mishnah (54a), if the Kaneh is not merely cut but rather the size of an Italian Isar coin is missing from the Kaneh, the animal is a Tereifah.)
2. Now to the question of the punctured Veshet: There indeed is a Machlokes Rishonim on this point. As you write, the Tosfos ha'Rosh maintains that Nekuvas ha'Veshet is only a Tereifah, but, as I wrote in my previous reply, Rashi and the Rambam maintain that it is a Neveilah. I propose that, according to the principle that we must attempt, wherever possible, to minimize the gap between different opinions in Halachah in order to narrow the dispute (see, for example, Shabbos 138a), since according to Rashi and the Rambam the animal cannot live even a short time because it is a Neveilah, and, in certain respects, is considered dead already, it follows that even though the Rosh maintains that it is only a Tereifah he still agrees that it cannot live for more than twelve months. Even the opinion in the Gemara that a Tereifah can live for more than twelve months will agree in the case of Nekuvas ha'Veshet that it cannot live, because it is highly unlikely that there could be an animal that, according to Rashi and the Rambam, is dead already, while according to the Rosh it will live for over a year! The reason why Nekuvas ha'Veshet is a Neveilah, according to Rashi and the Rambam, is that a Tereifah in the Simanim is worse. This is because the very life of the animal is dependent on the Veshet and Kaneh (which is why Shechitah must be done there -- in order to remove this life). Therefore, even according to the Rosh, it is likely that the animal will already be dead by Pesach Sheni.
Yeyasher Ko'ach Gadol,
Dovid Bloom