I know a company (and its founder) who did exactly that, with success. Apparently research institutions have some buffer funds, and if they have a decent chance

I know a company (and its founder) who did exactly that, with success. Apparently research institutions have some buffer funds, and if they have a decent chance of getting more funding, will use them to commission such services. What they did was writing the proposal, proofreading and editing input supplied by partners, then taking a share in the project and dealing with management and documentation. Pretty much exactly what you describe here.