I think that you would have a great story to tell to future interviewers if you can get the bad code under control and launch the product (even if the startup fails). I would have more confidence in someone who overcame adversity than someone who never faced any problems.
The "+2.5-3 sigma technical and +3-3.5 sigma big picture" stuff would be a big turn-off to me. There's a lot of really smart and talented people in this industry.