If they canceled your administration, I think that they would most likely give you a fee waiver for a future LSAT, but it would not have the perks of the July 15th LSAT (being able to cancel your score).
The only thing you have to lose by applying to T14 schools is the cost of the application fee and the time spent preparing the apps. I'd say focus on the LSAT, shoot your shot, and be willing to apply broadly