Constant:

But, without going into details, I hastily extrapolate that if the fish is a poorer conductor than the seawater, then it is better for the fish to be oriented parallel to the flow of energy (i.e. facing the lighting strike point, or facing away).

You are correct! I hastily analogized from the human step potential, ignoring the fact that fish, unlike humans, may well be much poorer conductors than the surrounding (or, in the human case, underlying) medium. Sadly, it seems the electrical engineering courses I took long ago haven't left many surviving correct intuitions.

After a bit of googling about this question, I'm intrigued to find out that the problem of electrocuting fish has attracted considerable research attention. A prominent reference appears to be a paper titled Electrical stunning of fish: the relationship between the electrical field strength and water conductivity by two gentlemen named J. Lines and S. Kestin (available ungated here, and with a gruesome experimental section). Alas, the paper says, "No publications appear to be available which identify conductivity measurements of fish tissue at the frequencies being used." It does however say that we might expect something in the hundreds or low thousands of uS/cm, whereas Wikipedia informs us that the conductivity of seawater is around 4.8 S/m, i.e. as much as 48,000 uS/cm.

So, yes, this was definitely a blunder on my part.