So... what's the best way to kill these buggers now that combat doesn't work at all while swimming/diving? I want their scales! The water is not transparent enough for me to see them while attacking from land either.

They're tricky, but you have to draw them to the shore, then attack them. I haven't tried magic, but it might work better than melee weapons.

Sometimes they come out of the water and glide across the ground, if they don't do that, use a fire spell or an arrow on them.

In the once-wise words of Festus Krex, fireballs.

You'll come across dozens of atronach scrolls, or alternatively learn the actual spell.

Flame Atronachs are the snipers of Skyrim's world, try that.

I put heavy armor on, smear myself with slaughterfish pheromones (optional), swim around the swamps south of Solitude until 3 or 4 are on me, then head to a shore shallow enough where I can wield the weapon, then play whack-a-fish