I believe a portion of a paper I am coauthoring is false
You seem to be giving two stories: you note that you 'still believe the conclusion of the paper is true' but you then note that 'it is dishonest to publish something which I believe is not true'.  If the issue is simply the handling of the data analysis (with alternative paths leading to the same conclusions through more or less fancy approaches), I might suggest a compromise. Add a footnote at the presentation of that analysis indicating that conclusions remain even under a more conservative statistical analysis.  If the journal allows, you can elaborate a bit there.  That way, you've solidified that you understand there are multiple approaches, but the conclusion is robust to that. This might be even more convincing.