Hi Emily, thanks for the question.  

If you can, remove the plugs from the good cells and place them a clean, sterilized tray and quarantine them. Dispose of the bad plugs.

Damping off seems to get us all sooner or later.  A good sterile soilless mix and sanitized trays definitely helps.  Cool wet soils can provide the environment for the pathogens to thrive. Don't plant too deep.   Heat mats can increase the temperature of the soil as can watering with warm water.  Watering from below is beneficial (i.e., Water by placing the seedling tray in a leakproof tray and adding water to the lower tray. Allow the water to wick up into the soil for about 5 min.  Dump excess water.).  Soil should not be soggy.   Some growers use a light spray of a dilution of 3% peroxide (1 Tbs per quart of water) on the soil surface to control the pathogens.  Adding a fan for air circulation can also be helpful. Check out the following links for additional info:

• Damping Off (psu.edu)
• Damping-off in Flower and Vegetable Seedlings | NC State Extension Publications (ncsu.edu)
• How to prevent seedling damping off | UMN Extension

I hope this helps:

This is SO helpful, thank you! A follow-up question: How far distance-wise should the quarantine be (a few feet? in another room? I ask because all my lights are set up on a tall utility shelf, so unsure if I need to make another light table elsewhere in the house) as well as, how long should those seedlings stay in quarantine (a certain length of time, or perpetually until they can be planted out after last frost?). 

Emily,

Good question!  It would be ideal to keep them in different rooms; however, that's not always easy to do.  You could put a physical barrier between them and the other plants.  Make sure you are careful not to pass pathogen through tools or handling.   Once you get two sets of true leaves you should be fairly safe since more mature plants are less susceptible.