T.A. 3019 August 28: Saruman overtaken between Sundown and Moonrise

Since the moon is only a few days from full on this date, then a waxing gibbous moon would have been rising in the southeast during this encounter at sundown. Maybe even appearing above the mountains around the "Treegarth of Orthanc" from this vantage. You can see the same kind of moon rising at sundown tonight!

T.A. 3019 August 22: The disbanding of the Fellowship of the Ring at sunset

When they take leave of the "King of the West" at sunset, there also would have been a broad, waxing crescent moon out in the southwestern skies, just a couple of days from its first quarter; just like today!

T.A. 3019 August 10: The Funeral of King Théoden

Just like today, the funeral of King Théoden took place the day after the moon's 3rd quarter... The day of the funeral was also the 1st day of "Autumn" (Yávië/Iavas) by the Reckoning of Rivendell in T.A. 3019, or Urimë 18 by Aragorn the King Elessar's New Reckoning.