According to "tradition", which I know must be verified, on Jubilee years the Head of the Year is moved to the Day of Atonement. So the combination of Head of Year + 10th day of the month is what many other people interpret as a Jubilee.
Standing on its own, I agree that it is softer than I would like, but because it aligns with the other evidence from the temple construction I view it as a reasonable second witness.
So what you are really asking for is evidence to support the tradition. I would love to see that evidence as well.
If there was a conflict between these two then that would be a red flag to consider more closely.