appears to be “You don’t. What you need is an Ideas Splurge.”
Giving away the punchline: In crude terms, an Ideas Splurge generates more well-thought-through ideas per person in less time. More people meet and talk in less time. It is more inclusive, and less off-putting to newbies. It can be arranged at shorter notice, and there is less to go wrong. It leaves folks wanting more, rather than, as with many hackathons, “well, I’m glad that’s over”. An Ideas Splurge is, fundamentally, more effective at tackling the disconnects between disparate groups within a company.