Ways to kill/remove things that live in dirt:
Constantly uproot (digging thing?)
Poison (yeeeah, no)
Starve (maybe?)
Manually attack (nope, too many. Could be satisfying, though)
Add predator (what eats worms? Blue crab?)
Remove dirt (probably not)
Sift dirt (doubt that's doable)
Strangle/smother (not sure how to accomplish that, probably bad idea anyway)
Constantly annoy (maybe)
Nuke (nope)
Got another idea. You'll need some kind of plastic mesh that's large enough for the worms to crawl up through, but small enough that a worm crawling around on top will stay on top if you pick the mesh up. Place the mesh over an area of the sandbed and aim a powerhead or similar at the middle of the mesh. I doubt they'll like that. Theoretically, they'll crawl up out of the sandbed in order to go somewhere else. I doubt they can move fast, so you'll have lots of them on the mesh after a bit. You could then just pull the mesh out, dump the worms, and put it back in.
Ooh- arrow crab would most likely eat them. Arrow crabs are known to eat tubeworms and similar. You'd have to get a large arrow, though, and they eat small fish...
Perhaps a combination? Remove the fish and don't feed the tank, plus add a couple of large crabs? The lack of food should make them crawl out to look for more, and the large hungry crabs should finish them off pretty quickly.
For manual removal, what about a kitty litter scoop?
Or, hmm... get a powerhead and set it up so that it blows across the sand to keep gunk from settling at all. Also add some filter-feeders, or maybe just a good mechanical filter, to get the gunk out of the tank before the worms get it. Get some long tweezers to pick them out if they start crawling out to look for food.
Or give in and just plumb a sump full of chaeto in there to deal with the extra nitrates.
Just realized we're all just sitting here plotting genocide.
We have lots of ideas.