Yours is one of those rare cases where your soft factors may very well come into play. Usually they don't, and the numbers determine your admission/denial almost exclusively. Hence, it's pretty easy to gauge your chances. The funny thing about being a splitter is that your admissions chances can be very unpredictable depending on which schools you're applying to.
175 is a fantastic LSAT score, and is probably sufficient to get into just about any school outside the top 25. The truly elite national schools (Harvard, Yale, etc) are probably out of reach with 3.0. Thus, your "battleground" will likely be the schools in the 15-25 range: UCLA, USC, Notre Dame, etc. If you look at the admissions grids on LSAC, you'll see that at many of those places the statistical probability of someone with your numbers being admitted ranges from 25-75%, depending on the school. This means that in similar situations those schools are looking at factors other than just GPA/LSAT. Youmight have a big advantage with your background.
Another possibility: depending on what you want to do after law school, and considering any applicable financial/family/personal concerns, you may want to consider seeking a full scholarship at a lower Tier 1 or Tier 2. A 175 LSAT is probably enough to pull off a full ride at many such schools, and the lack of debt may be more beneficial to you in the long term than a higher ranked school with a hefty price tag. If you get into an elite school, the cost may be worth it. But if it's a choice between the #24 school at full price versus the #37 school for free, you may want to carefully consider factors beyond rankings.
Good luck and congratulations!