Make sure all participants understand the rigors of the process, i.e. many meetings and then wait. Set a deadline for participation and require an institutional commitment from the administration of that institution. It then appears more cooperative than if the PI types it all. These people also might know sources of funding that would be appropriate to your project. Get help from your institutional grants or development office on all technical details of the submission.
Most grants require institutional signatures and are handled by a specific process.
If your institution has no grants office, collaborate with someone who does have one. Know your NLM or other grant program. Read the call for proposals and use the same words they do. Talk to the grants officer at the funding agency. Work closely with them if your institution has no grants office.