Why Yom Kippur is on the 10th? This date does not make sense! If you search through the Written Torah, you will see that nothing happened on this date. Wouldn't it make sense to have Yom Kippur on the 8th? All sin atonement and sin offerings take place on the 8th or on the 8th from some event. There is absolutely no connection to number 10.
For example, offering on Yom Kippur in Numbers 29:8 is the same as the offering of the 8th day of Sukkot in Numbers 29:36. I think this is the best textual argument for the 8th being the correct date of Yom Kippur.
Even the Moon is in phase on the 8th. On the 10th the Moon is between phases and therefore meaningless.