To be honest, I think this is the best you can do if you want a professional-type career. Getting consulting jobs out of law school is doable, especially from SLS. Unlike banking, consulting cares more about your analytical ability than anything else, WE is a plus for them, but given that they hire tons of liberal arts grads from elite schools all the time solely for performing well on their case study method (seriously in college I knew multiple theater majors who got jobs at MBB), this is like a second chance to get that. Consulting wants JD's because they value diverse backgrounds and approaches to problem-solving, they wouldn't be recruiting at law schools if this were not the case. Also, if you spend the time between now and law school prepping for the GMAT, you can take that and potentially apply for a JD/MBA at SLS (I'm assuming you can do decently on that given that you did well enough on the LSAT to get into Stanford. I may be wrong if you are absolutely terrible at math, but most people can learn enough math for the GMAT and if you ARE that bad at math, you probably should just settle for law). Also, you should start prepping for case study interviews sooner rather than later so by the time the hiring process starts you have that skill down cold.
That said, given that you have very little WE, I don't think that consulting offers a radically different lifestyle than law. Both require grueling hours and a lot of repetitive work (at least in the early stages). It sounds to me like you just want a professional job, which law can offer just as well as consulting. Similarly most people aren't consultants at MBB or big law lawyers for their entire lives. Either path can get you a corporate job if that is what you realize you want to do (its definitely easier from consulting, but not terribly hard from law). Most people aren't going to LOVE their jobs anyways.
I will say to those who think no one should go to law school without actually wanting to be a lawyer, they are mostly right, but in this case, where the person only has a liberal arts BA and merely wants to launch into a professional career after years of medical problems, law school makes sense. Getting a professional degree from a top school is probably the only way he is going to be able to do that at this point and it gives him a chance to start over and scrub the past. Since he would never get into as good of a business school as a law school and he's going to Stanford with financial aid, this decision is probably the best way to meet his goals. I also don't think an interest in practicing law is a prerequisite to doing well in law school. It certainly helps, but law school is still far more academic than it is practical, so if you attack it with the same gusto you attacked your BA with (once again, SLS is hard to get w/o that) you should be fine. The material is interesting enough and the main thing forcing most students to work hard is that its a means to an end. Just because for most people that is a legal career, doesn't mean that getting a job at MBB or getting into the joint JD/MBA program at Stanford can't light a similar fire under your ass. Anything can be interesting provided you have something to motivate you.
TL;dr: Getting MBB from SLS is totally doable, provided you prepare for the case study interviews and commit to the process. Consulting is the one business area where WE is not a huge requirement. Look into maybe doing a joint degree once you are at SLS (this will be easier if you kill first quarter, even with their modified P/F system). Be open to a career in the law, you might not think its great now, but for most people the pros and cons are similar to those for consulting and it doesn't close off a corporate career in the future. In your specific situation (medical issues, no WE, 28 years old, liberal arts degree, wants professional career, in at SLS probably with financial aid) law school is not a mistake, even if you don't really want to practice law. 99.9% of the time going to law school w/o wanting to practice law would be a mistake, but you are that special snowflake where going to law school makes sense and is probably the most efficient way to pursue your career goals at this point.