Deadlines that are close to each other create a lot of stress. I have a February 5, a March 5, and a March 2. For the March 5, I have had to get a preliminary draft done four to six weeks before. Some people might deal with this by just working to meet the deadlines in sequence, and not worry about the later ones. My approach, however, is to make sure that once I meet the Feb. deadlines, I will be in a position to do the March ones very quickly. That entailed making a list of the elements of the March 5 one and seeing if I could take care of some components earlier. My attitude is that I'll be as busy in the future as now, so that there no point in postponing something to a time when hypothetically I won't be quite as occupied. I avoided distracting multitasking by finishing discrete portions of the grants during particular times and days.
So for the three grants,
I have the NEH Seminar proposal 1st draft of the narrative description, which I've sent to the NEH for a first review. I've also filled out some other forms relating to this and made some calls and emails to people.
The internal grant for summer salary: I've written a version of the narrative and filled out the form except for the abstract. I can finish it easily when I get back from Spain, and revise any glitches in the prose.
Another travel grant from the university: I've made a list of components and warned the chair that she'll have to write a letter. I did the two-page cv.
When I get back from Spain I can then meet the deadlines in order, having done a lot of preparation for each one.