I just dealt with this on Saturday. I gave all of mine some Wazine in their water and about an hour to an hour and half later they were pooping exactly the worm you described. Talk about GROSSED out. I believe the eggs are still fine though but obviously, once you start the wormer you have to wait the usual 14 days or whatever the bottle says.
If I were in your shoes, I'd just give them the wazine (1 T per gal water) and then follow that up 10-14 days later with a broad spectrum wormer. I'm doing that... waiting for the 10th day or so. Hate throwing away those eggs in the meantime...
Oh, once I noticed the wazine kicked the worms out so quickly, I hung out in the coop and scooped up the wormy poo's... those chickadees love worms regardless where the worms are so I didn't want anymore nastiness going on!
