Parasites?

tiny worms

Clean the tank, hoover the gravel as best you can, and change your filter material. Change or clean out your filter material regularly, and often. Avoid overfeeding. They are usually in the tank but sometimes their numbers increase, perhaps due to overfeeding.
 
...a millimeter long and moving like inchworms... I can't even remember having eyesight that sharp, guys. You can rule out nematodes from the nematode movements, a ceaseless thrash thrash thrash.

I don't usually see Naidid worms except among gravel grains or up by the surface.

Try http://www.microscopy-uk.org.uk/ for some Aeolosomatid and some Naidid worms and other pond life that turns up in the aquarium too...
 
most of them are that small, there are others that are larger, much larger maybe 3-5 mm.
 
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