I have had a look at a Karaite source. To my great surprise, the Karaites agree with the Rabbanites on the Jubilee. Both maintain the first of the seventh is a New Year for certain purposes. The Rabbanites say Creation was on the first of the seventh. Note that this means there is no necessary connection with the date of the crossing of the Jordan. Actually the Rabbanites maintain that counting started after the passage of 14 years from Entry, with the first shemittah being in year 21 of entry.
The Jubilee is not in the lists of disagreements between Pharisees and Sadducees. If there had been disagreement it would have come up.
The reference to the Samaritan commentary on the Torah is unpublished. Refer to Boid's book Principles of Samaritan Halachah for details of the mss. I have used two, in Berlin and Uppsala. The writing of commentaries is cumulative over the centuries, so there is no invention in this commentary, only systematisation. I expect to find the Jubilee as a section in the Book of Commandments from the 14th c. or one of the compendia from the 11th c. but these are unpublished and there isn’t time to search through the mss. I will try to do this after finishing the appendixes if there is still time. Explain to the reader that I have condensed and slightly re-arranged the translation because the original repeats itself as it interprets each phrase.