1) If you get a 173+, you certainly will have a shot at several top 14 schools, even with a 3.37 GPA. Check out lawschoolnumbers.com for more specifics. Your soft factors will certainly play up your application.
2) Although you may have rocked those practice tests, understand that the strong majority of LSATers will score under their practice test scores. I'm not saying its impossible for you to score in the range you want, but it will be harder than you think. My best advice is to quickly review a test prep book(s) like Kaplan or Powerscore.. then take every single PT under exact test conditions until test day.
3) The difference between a 3.37 and 3.4 is exceptionally nominal. I think your time would be better served trying to get about 3 points on your LSAT or even writing stronger essays. Now, if you can get a 3.5 or 3.6, then thats another issue, but three one-hundredth of a decimal point is not all that alluring. On top of that fact that you will HAVE to get perfect scores in those classes. Which, based on your current record, may be harder than you think unless you take throw away easy classes. On top of the fact that you will have to explain to Columbia why you postponed graduation to take basketweaving to bump your GPA... Just my thoughts.
4) Although law schools really like seeing people overcome hurdles, be them external or self imposed, they also want assurance that the hurdle is FAR behind the student. My only concern with the drug issue is time. Although nine months is certainly very commendable, it is not in the same ball park as saying you have been ten years sober. If you are going to discuss your drug problem, then, you have to have several other hard pieces of evidence to substantiate your claim that it is really behind you and you have grown because of it. Have your grades improved drastically since you became sober (i.e. straight Ds and Fs to now straight As and Bs)? Finally, placement will be key. Although addendums are exactly what this kind of thing is for, you may decide that having a short paragraph in your personal statement is easier to acheive the above. You will be able to keep what you say more broad/vague, add luster to your personal statement, and still get the benefit of talking about a personal hurdle you overcame. Just a thought.
5) Finally, apply to more schools that just the top 14. Although there are certain perks in the top 14, it is not exclusive to them. If you know where you would want to live/work, apply to all the top full time and part time schools in that region. If you have a specific area of specialization you want to pursue (i.e. intellectual property), apply to all the top schools for that, even if the schools aren;t in the top 14. Not only will this give you more options, if you end up scoring as high as you hope, you will be able to snag strong scholarships (i.e. full rides). You may then be able to use those scholarships to negotiate for money at schools you would really like to attend (even some in the T14).