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There is an enormous difference between 168 and 172. Im a URM with a 167 and got $$ at a T20. I did not get into UT, and im a resident.

Your stats will be better. You are in good shape. a 3.5ish + a median or above LSAT + URM = great shot across the T14

If you have not already, have some fun here: Lawschoolnumbers.com

If your LSAT gets high enough you have a shot at everything minus Yale. Stanford won't be completely off the table (but not likely either) and you can actually have a very good chance at hitting H with a high enough score.

As a splitter, even a URM one, you're unlikely to get much money thrown your way so you really need to get into the best school possible. If you aren't PTing well into the 170s I'd probably plan on taking it again in the fall - you're leaving a lot on the table by going to UT/USC and shouldn't even consider SMU and L&C.

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Yeah there's quite a difference between 168 and 172. 168 nabs Cornell and GULC (in your case UW), 170 and 3.4 opens all of the lower T14 (and in your case UT). Above that makes you very competitive for T6

I'm going to disagree w the Harvard and Stanford comment, above. You'll need an astronomical LSAT for those w a 3.4. Not impossible, though.