Would it be considered unethical to submit the paper to a different journal while listing who we think the reviewer might be as an opposed reviewer stating that we have a conflicting approach to our particular area of research and feel they might not comment fairly?
Of course it is unethical. What you are proposing is to mislead an editor in order to circumvent normal peer review and get your paper published despite appearing to have a fundamental flaw.
The proper course of action is to modify the paper to clearly explain why this apparent flaw does not actually invalidate your results. If this reviewer thought it was a problem, and an editor agreed, probably others will too, so this is worth doing even if you don't get the same reviewer again.