Don’t believe me; believe Seth.
The last minute is not a buffer zone,
nor is it the moment to double-check your work.
Before that last minute, set aside a few hours or a few days at the end (the amount depending on the length of your response period) and hold it free of any planned work. Having this explicit management reserve is an essential tool in meeting schedule, which is the most-important thing in Proposal Land.
Good proposal teams schedule time to check their work, more than once and yes, at the end. They also allow time for things to go off the rails. Because they often do. And if they don’t consume all your management reserve? You can have a little more time to add to Seth’s last minute to admire your handiwork and your project planning.