Superluminal observations is a good point of comparing false science claims with false religious ones. Unfortunately, I don't know very much about the experiments. They haven't been emphasized enough by the scientific community for me to recognize their relevance to the fall of SR and GR. There are several points to emphasize.
1. What it is that is superluminal is controversial. Phase velocity was always known to be faster than c, whereas it is group velocity that must be less than c.
2. It's possible for physical objects such as electrons to travel faster than light in a medium other than vacuum. Cherenkov radiation is one result.
3. If you send a repeating signal it can be less clear when one part of the signal reaches the other end.
4. If the results were as secure as you suggest why is it taking so long for science educators and GR/SR theoreticians to change their tune?
5. Most important: Science is based on experimental evidence. What you see is what you get. If observations prove scientific ideas false then new ideas will replace them. Quantum Mechanics and Relativity developed, not because they were more intuitive than Classical Physics (they're a lot less intuitive), but because they better matched observations. Big Bang cosmology is accepted today, not because it's more elegant than an unchanging universe (it isn't), but because it better explains the observations. Religion doesn't work that way. Religious people are not supposed to summarily reject religious claims that have no rational support but are expected to accept on mere faith, without observational confirmation, a wide variety of superstitious and unbelievable things. Religion and science are very different in how they deal with experimental confirmation of their tenets.
6. As several have emphasized lately, flaws in scientific understanding does not justify faith-based religion.
If Jesus didn't exist then I think we are justified in doubting all religious statements that have no experimental support, just like we should doubt scientific claims without experimental support. I expect science and religion to satisfy the same demands of the rational mind. If Jesus didn't exist then the existence of God is put into question. The existence of an afterlife is put into question. If Jesus didn't exist then it's reasonably possible that people who claimed to see God or "know" that He exists or have spoken with the dead could be deceived or lying. If a scientist lies to you there is experiment to set the record straight. What is there to set religion straight?
You've made a good point, worthy of further comment, but I was hoping for something more related to Zindler's essay. Do you have something to say about that?