The new experiment only eliminates one possible error - admittedly one that seemed quite plausible. So it is still too early to conclude that neutrinos are travelling faster than light. Although it appears more likely now.
Cavediver or Son Goku could probably tell you more. Your suggestions sound reasonable, but I do wonder if there are other possibilities. It would indeed take infinite energy to accelerate a particle with non-zero rest mass to c, if Special Relativity is true, so there must be some loophole and QM is a good place to look for it.
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