I think I finally found the right word: dissemble. It captures the meaning of both obscufating what you're saying and arguing something that you know is not true. It's something a sophist might do if he thought it was a tool that he could use convince you of something.
Verb (used with object), dissembled, dissembling.
1. to give a false or misleading appearance to; conceal the truth or real nature of:
to dissemble one's incompetence in business.
2. to put on the appearance of; feign: to dissemble innocence.
Verb (used without object), dissembled, dissembling.
4. to conceal one's true motives, thoughts, etc., by some pretense; speak or act hypocritically.
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