I made the mistake of over watering my fig cuttings and not noticing they were in standing water in the bin.  Hopefully I dried them out in time.

Tom,

Didn't watch the whole video ( speed right through it).
But an ice pick can be your best friend in this situation. Poke it right through the holes about an inch to unclog it and watch it drain.

Even a small screw driver or Qtip (after removing the cotton).

Looks like you saved them in time. I like to move the soil on the top around with a toothpick to help dry it out, when I overwater.

A very good way to get that extra moisture out in a hurry is to just push a piece of yarn up in to the cup through a drain hole.  The water will wick right out of the cup.