My lawyer told me to also get letters from people who didn't work with me and those were harder (4 month for one of them). Getting a letter from my former advisor took a day in comparison.
Mostly people don't have time, so just write them the letter to the point that all they have to do is attach their CV and sign.
My strategy was to ask 11 people for letters and by the time 8 were done I just submitted the application. I still haven't gotten the last 3 but I also stopped reminding them. Most lawyers seem to think 5+ is good enough anyway.
For me the most awkward part of this step was to write the letters for people. You have to call yourself "outstanding", "exceptional", "leader of the field", bla bla bla. Pretty annoying. I usually don't like talking about myself in superlatives.