I'm really bad at getting LORs, but I did manage to get them done.
My advisor told me that in general surgery, the letters need to come from surgeons, and the name of the letter-writer is important. I saw why this was true when I went for interviews - the interviewers would often read the letters in front of me, and they would only stop to read if they recognized the name. Thus, the letters from the "famous" surgeons were carefully read, while the other one was just glanced at, even though the less famous person knew me better.
I was also worried about asking for letters many months after the rotation. This was never a problem. Just be sure to send the person your CV, personal statement, and a brief note on any presentations/write-ups/whatever that you may have given to them, anything that might help them remember you.
If the name is important (as it is in surgery), then get the big names, even if you have to do an outside rotation to get them. Don't worry if it seems like they are ignoring you. I swear that 2 of my big-name letter writers said a total of about 50 words to me, but they both wrote great letters. Remember that people generally aren't going to screw you over.