Drawing on theories I laid out in the 1290 days post and Messiah The Prince post.
Jewish tradition says Elijah will return on Passover, that is part of the reason for the Elijah Cup. I would never build doctrine on Rabbinic tradition, but that happens to correspond towith many reasons I have for believing the 70th Week begins in Nisan.
Ezekiel 45 makes the 7th of Nisan important for some reason. Interpretations of the Chronology of Joshua often put the entry of the two spies into Jericho on the 7th of Nisan. If that is the day the Witnesses begin their ministry, then the 25th or 26th of Elul could be the day they're martyred, depending on if we count them inclusively. Placing their Resurrection on the Feast of Trumpets or the eve of it, and then the Seventh Trumpet probably that same day or the next.
If it does start on Passover, either the 14th of 15 of Nisan they begin their ministry on. Which could be the same day the White Horseman is formally crowned. Then their martyrdom could be the third of Tishri, which is the fast of the seventh month.
I also have a feeling The Image of Revelation 13 (which I don't view as linked to The Temple), could be set up on the 15th of Cheshvan. 1290 days before that could fall if they're counted inclusively on the 26nd of Nisan. That day is considered by Jewish Tradition the day Joshua died. If The Antichrist claims to be or is claimed to be Messiah Ben-Joseph, then Joshua is one of the people he'll be claimed as a type of him. And I now think it's possible his mortal wounding could be the same day the 1290 days begins.
That is assuming no Second Adar during the period, if there is a Second Adar, then that moves either the start of the 1290 days up to Iyar or the end of it down to Tabernacles.
If the Beast's resurrection (when I begin the 42 months he's allowed to continue) is in Tishri, 42 New Moons latter could put his demise probably in Adar.
If the 1260 days Israel is in the wilderness begins on the 25th or 26th of Elul it could end on the 17th of Adar. The last of the days affiliated with Purim. If it starts on the third of Tishrei then the 25th of Adar could be it's end. Jeremiah 52:31 makes that date potentially significant, many interpret that as also being the day Nebuchadnezzar died.
If we start the 1335 days with The Rapture, and it happens on the First of Tishri. Their end would be around the 10th of Sivan. If that day happens to fall on a Sunday, then it would probably be the day that Biblically Pentecost is supposed to fall on. Sounds like a pretty good day to start The Millennium.
My theory is that the 70th week formally begins on the 1st of Nisan, but the actual events that will make clear we've entered it will happen latter in that same Nisan.