1) I found, bs'd, that the Ibn Ezra (in Parshas Beshalach, Shemos 13:19) asks a more basic question. The oath that they would not strike them was taken only on condition that the Giv'onim had come from a far-off place, as the Giv'onim said (Yehoshua 9:6), "We have come from a far away land." When it transpired that they had in fact come from a nearby place, the correct action should be not to honor the oath, so that they and all Yisrael should not transgress (Devarim 20:16) "spare none."

The reason they kept the oath was so that the honor of Hash-m should not be desecrated.

2) To express this idea in slightly different language, we can say that it would be a Chilul Hash-m not to keep the Shevu'ah. That can also answer the question about Aseh Docheh Lo Ta'aseh. Even if one has a Heter to override a Shevu'ah, it is still a Chilul Hash-m if people will think that Jews do not keep their word.

3) I assume that the question here is that there is a Lav of "Lo Sechayeh Kol Neshamah" (Devarim 20:16) and an Aseh of "Hacharem Tacharimem" (Devarim 20:17), so these should override the Lav of "Lo Yachel Devaro" (Bamidbar 30:3).

However, Tosfos in Gitin (46a, DH Kivan) writes that the Lav of "Lo Sechayeh Kol Neshamah" applies only to nations that do not want to make Shalom, while the Giv'onim wanted to make Shalom.

4) The Chidushei ha'Ramban (Gitin 46a) writes that if the seven nations of Canaan would agree not to worship idols, then the lav of "Lo Sechayeh" would not apply. In this respect, the Giv'onim had done Teshuvah.

5) Here is an answer according to the Sefer ha'Chinuch. The Sefer ha'Chinuch (Parshas Yisro, Mitzvah 30) writes that every vow carries a negative and positive Mitzvah with it. These two Mitzvos appear in the same verse, Bamidbar 30:2. The negative Mitzvah is, "He shall not desecrate his word." The positive Mitzvah is, "He must do in accordance with what came out of his mouth." Since a promise is both a Lav and an Aseh, it follows that we do not say Aseh v'Lo Sa'aseh Docheh Aseh v'Lo Sa'aseh.

6) I should point out that the source of the Ibn Ezra, cited above, is Gitin 46a, where the Rabanan state that the oath to the Giv'onim never took effect since they said that they had come from a far-off land but this was untrue. The reason they did not kill the Giv'onim was because of Kidush Hash-m. Rashi explains that this was so that the Ovdei Kochavim should not say that they transgressed the Shevu'ah.

Dovid Bloom