Grant drafts fail in committee because the aims are mush or the budget tells a different story. They do not fail because a colleague did not read appendix D.
Ask for a review of one of those two.
Put the section in the briefing
Specific aims, as text. Or the budget lines that changed. A link, in words, to the shared draft they already have. No attachment.
Say what you already know is weak. That is not humility theater. It aims their time.
The deadline is the agency's, not yours
Say the real date. If they cannot make it, you need that no early enough to ask someone else. A soft "no rush" here is how you submit the weak version.
They were not in your session
Your assistant has been cheerleading the significance section for an hour. That context does not transfer. The colleague needs the aims and the question: where would a reviewer stop believing you?
Academic collaboration is the longer form of asking across labs. This is the shorter one: one draft, one section, one Friday.