"CLAIM 6) The truth of the oral law given to Moses could only be in one opinion, not many opinions, if it existed.
That is correct. The Oral Instruction from Sinai was not disputed in the Mosaic Court. The Talmudic Sages agreed as to what the Oral Instruction from Moses constituted. For example, there was no disagreement among them that the Oral Instruction regarding the command to bind frontlets between one's eyes was that the command is not merely metaphorical. There was only lack of clarity regarding a few details of the Oral Instruction from Sinai, such as some minute detail of how the frontlet is made - and the conflict of opinion was not considered due to multiple opinions originating with Moses, but rather due to the great turmoil and and distress of the last generations - the increase of persecutions and heresies. In the case of conflicting opinions, the majority ruled, in accordance with the solution to disputes that is commanded in the Written Torah. The vast majority of Talmudic debate is over clarification of legislative rabbinic law which is to be applied in new situations - NOT regarding the Oral Instruction from Sinai. The distinction between these two has already been elaborated upon.
CLAIM 7) The Mishnah does not solely speak in the name of Moses.
This reason for rejecting the Oral Instruction would only be valid if the premises of this argument were true, but it is false. The Mishna does not claim to speak solely in the name of Moses. This argument is based upon a misconception of what the Mishna is, and its purpose. This has already been elaborated upon. One can not justifiably reject a thing due to a reason that is not true concerning that same thing.
Why don't Karaites have a problem accepting the Book of Proverbs, the Book of Psalms, and a number of other Biblical books which do NOT contain the words ""Thus saith the LORD"" nor speak in the name of Moses - but this suddenly becomes a problem for accepting the Talmudic texts?