My range of deadlines was Dec 1 through Feb 1, so not as long as yours were. I don't think they were upset because professors generally write LORs over a 6 month period anyways. Most postdoc applications are due between Oct 1 and Dec 1, then US grad schools usually Dec 1 to Jan 1 and most Canadian schools between Jan 1 and Mar 1.
You should get in touch with potential LOR writers ASAP. If you are currently in school just stop by their office during office hours, tell them you are applying to graduate school, and then ask if they would be willing to write an LOR on your behalf. If you are not in school then just shoot them an email.
1. Don't wait to the last minute to notify your LOR writers. Professors have a lot on their plates and may not get around to writing the LOR, let alone sending it, until weeks later.
2. Work on both simultaneously. If you are a senior in college, or have already graduated, you surely can find at three former profs/PIs willing to write LORs.
Professors do prefer to fill out the forms at once but December to May is a huge difference. Maybe your program is different but you will likely hear back from the December 2014 deadline school before you even reach the May 2015 deadline. Personally, I separated the LOR request into two phases. The first phase was the initial request / heads up that I would like them to write letters. This happened around this time of year in 2011 for me. I informally asked them if they would agree to write a letter. By the end of October, I had a one page summary document with my info at the top and then a list of schools, sorted by due date, and also a few names of people I wanted to work with.
The second phase is submitting the actual request from the application itself. My LOR writers let me know that they would likely not be submitting the LORs until the deadlines were closer (since they are busy with classes in the fall). I made the formal submission of their name to the application about 1 month before the due date which generates an automatic email. I did this in batches--so I did one on Nov 1 for schools due between Dec 1 and Dec 15, one batch on Nov 15 for schools due between Dec 15 and Dec 31, and one final batch on December 1 for schools due after Jan 1.
I chose to do them in waves so that the profs won't get all 8 schools at once but also won't get 8 sporadic emails. Also I figured that the Nov 15 batch would remind them that I had submitted an earlier batch a couple of weeks ago. I sent another reminder (through the application's reminder system) about 2 days prior to the due date. For most letters, I got them either on the due date, or about 2-3 days after the due date (it's almost never a problem).