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With the money left, maybe a smart fund-raiser could get some conversations started with bigger donors who could match grants and go in a large round. The money might buy you the time of a Bruce Schneier or Richard Stallman to advise and promote the project in its infancy. And non-profit software orgs are underpaid and work on shoestring budgets already that this is real money to them.
The experts shouldn't write any line of code, use the community as code monkeys, only accepting pull requests and merge them in the project(basically what Linus does this days). Would that not be feasible?
I don't see this as the roadblock. They (the experts) could bill by the hour. The most intensive period is the initial specification/design/architecture. After the burst period they just have to review the commits for security pitfalls and merge them if OK. The community could have some volunteer reviewers for triage.
I have no idea if this actually works and I also didn't heard anything like this done before, so take it with a grain of salt. That's why I asked more knowledgeable people how feasible this could be.