Re-analyzed my dissertation work, how should I explain this in a cover letter to a journal editor?
Your submission to the journal will be a separate paper to your dissertation, so it is not a problem if you revise the method and get slightly different results.  Just undertake the analysis with your new method, and write that analysis up in its own right in the new paper --- the journal referee will assess this work on its own merits.  Normally in this case you would cite your dissertation as a precursor to the work in your present paper, but note that your analysis differs from the analysis in that work.  (Perhaps explain this briefly in a footnote.)