A hackathon for performance improvement screams to me "you'll be re-interviewing for your own job." I don't foresee this going well for the company. Best case scenario: you wildfire churn all the chaff engineers which limits the company's throughput until they're rehired... with no expectation the new hires will be any better. You also lose A LOT of domain experience and are self-inflicting brain drain.

I'd try and push for some "lunch and learn" meeting where the engineers get lunch catered and in exchange sit in on a meeting where you explain your point of view. Without monetary incentive it'll be hard to change the culture, but not impossible (and food goes a long way in greasing the wheels).