Jacy, although I agree that any part of the application package should not be overlooked, I must say that I do not believe LORs to be of vital importance; I would say that it is the least important part of the package. The only thing one needs to make sure is that the professor will not write a negative LOR, as it is often known to happen. This can be easily accomplished with a simple question asking the professor whether they will be comfortable with writing a LOR for you. Unless the professor is sadistic, they will usually voice any hesitation to write a LOR for you, so it's nothing to worry about. What I was trying to convey is that one must focus on obtaining an awesome LSAT score and writing a memorable PS rather than worrying about the dynamics of their LOR. I'm sure that two more points on the LSAT will overcome any mediocre LORs.
As for competitiveness, I assure you that the Economics PhD programs at MIT, Chicago, Stanford, Yale, Harvard, Berkeley, Minnesota, LSE, and so forth are much more difficult to get into than most law schools. Law schools admits about 400 students every year, a PhD program admits about 5 to 10 students, and a Masters program admits 25 or so students.
You're really lucky to have had multiple class sizes of 20. I'm assuming that BU is private? I don't think I've got to know any of my professors other than asking them "sir, do I have to know this for the exam"?