I really can't imagine a school preferring a 178/179/180 to a 177 in any significant way. The higher score would not do any more to help their median/quartiles, and the number of people scoring above 177 is so small, there is 0 chance that one of them pushes you out. I guess it might help you with a school's "index" formula, but seriously, with splitter stats like yours, I doubt that holds much weight.
Plus, not all schools take the highest, and even among those that do, if you retake and somehow screw it up (or even just drop a few points), it makes your 177 look like luck rather than as impressive as it does on its own. I suspect your application will get a lot of individual attention due to uniqueness, so give them as few reasons as possible to turn you down.