Based off of what you said about your performance on the sections of the LSAT that you were able to complete, it definitely seems like going to Texas Tech would be selling yourself short. Liking the school and the people are one thing, but it doesn't make up for poor placement numbers. If you are missing virtually no questions on the LSAT you should obviously be in a T14 (or USC/UCLA). You mentioned earlier that you didn't want to waste another year with retaking/reapplying...
What would you think about this solution? Signing up to take the test again in June. That way you take the test again and if it goes poorly, you go to Texas Tech as planned. If you do much better (say 160+), you then withdraw from Texas Tech and reapply next year knowing you will have much better options. Also, in case you are wondering, a lower score in June (or even taking the test while already accepted at Texas Tech) will not hurt you with them at all. There is no risk of them taking away your acceptance or anything like that.
If you got to 160+, with your background/soft factors/medical addendum, it seems like you should send an app to Berkeley. If anyone would be willing to look past numbers, it would be them (plus they are a public school so tuition would be free).
I'm not familiar with your medical condition, but is there anyway possible to score higher/get through more sections? Could you power through the first 3 sections, guess on the next one (basically giving yourself a 45 minute rest), and then be recharged enough to do the 5th section?
When a lot of people prep for the LSAT, they focus on learning to answer the questions. You seem to not really need help with that, its more of an endurance issue. Since you know the accommodations they will be providing you, is there anyway you can practice different strategies under those time constraints to see how best to maximize your score?
You said you like overcoming challenges... seems like finding a creative way to dominate the LSAT (which you are clearly capable of doing) would be right up your alley.