How much energy is "stored" in a magnetic field where |B|=0?
The energy is not stored at that exact geometric point, that's just where the lines actually cross. The magnetic field is nonzero in a large region around the crossover, and that's where magnetic energy density is nonzero and that's where the magnetic forces are acting. Nobody ever said that the energy comes from the *lines themselves* at the exact point of crossing. There's a wholesale rearrangement of nonzero B fields from one orientation of "saddle" to another. In the middle of this rearrangement is a point where B=0 and lines reconnect.
Similarly, if you build a four-pole quadrupole capacitor, there's a spot in the center where electric field lines cross and where |E|=0. Is there energy density in these fields? Of course. If the pole pieces weren't mechanically pinned down, would they accelerate under the influence of electric forces? Yes. Where would the kinetic energy of the moving pole pieces have come from? From electric field energy density in the space between them, including near the E=0 point.
I would have been sympathetic to a claim, if you had made it, like the following: "When these magnetic reconnection topologies occur, the mainstream model says that the lines "run away" rapidly and spontaneously; my work shows that reconnection is a slow process that doesn't proceed spontaneously/doesn't change the magnetic field energy/moves magnetic fields around but doesn't couple to particle energies" I would have no particular scientific objection to that, except insofar as I know that a large number of smart people, doing careful numerical work, get the opposite result. It would not lead me to label the arguer as stupid, childish, or a crackpot.
But you never made such an argument. You argued that field lines cannot break (nobody ever said they could), then that they could not cross (but they can), then that there's no energy density at the crossing point (why would there need to be?). You made a bunch of arguments, in other words, that could only come from someone who didn't know much E&M but knew only that they need to conclude, somehow or another, that reconnection is broken.
And next month you're going to be back saying "Alfven was right because lines cannot break" and we're going to go through the whole thing again.
