A synaptic cleft is like 40 nm, or 10,000x smaller than 400 microns, so it seems the scales of typical communication are enough orders of magnitude smaller to be an implausible explanation?

If the signal transmission worked at 400 microns, I would say that your feature size argument would be a good reason to consider other explanations, but they explicitly show that such a gap prevents the signal from being transmitted.

Instead, the transmissible gap is poorly characterized—-they cut then stick the slices back together. Depending on how clean the cut is, the gap could be quite small. Yet they argue that this unknown small distance (which presumably still contains a fluid interface) is enough to eliminate the usual explanations. That argument feels undersupported to me.

Ah, I was under the assumption that 400 microns was implied to be at least within an order of magnitude of the threshold, so for example I assumed the signal transmission worked at at least 40 microns, which is still 1000x the synaptic cleft. If there's no information about where the cut-off is, only some upper limit, perhaps even due to the lack of precision in the technique itself, then this does seem pretty questionable, indeed.

Or, furthermore, by standard induction, or by standard conduction via the extracellular matrix (assuming the ECM can deal w/400microns and axons/dendrites cannot—idk if this holds)