First, they aren't magic. Reasoning by similarity (magic) is not the way engineers make progress. If Watt reasoned by similarity he wouldn't have seen the relation between a horse and a steam kettle. Now, if somebody wants to build an FTL ship, he needs to find something other than electric, magnetic, or gravitational forces to drive it. That's where physicists work, looking for signs of something going on where everybody has been looking but seeing nothing. Nothing propelled by EM can exceed the speed of light, it's not in the cards. But, ordinary matter could exceed c even though it has electrons and protons and therefore EM effects. Electrons and protons are not EM phenomena even though they exhibit EM phenomena under certain circumstances; something else could possibly drive them to FTL speeds and possibly very easily. The mass, time and length problems are specific to EM phenomena. The math used is that of solid state mechanics--very strange if you think about it.
"First, they aren't magic."
Exactly.
As for your whole paragraph, I completely agree. I find it encouraging that the FTL community is slowly gaining respectability, as humans tend to be able to figure out ways of doing things, if they can wrap their minds around the required concepts.