I notice nobody offered to help so here is what I would do.
Make a new egg box; use a larger tupperware container that will accept another box that is big enough to hold the eggs. Into this Large container put about 2 inches of perlite, pour water into this until the level is about 1/4 inch below the surface of the perlite, now take the smaller container, fill it with DRY perlite again a 1-2 inch layer, and place the clutch in there. Put the smaller container in the larger one, place the smaller one on top of some little spacer that will lift it about 1/4 inch above the surface of the wet perlite in the larger container. Place a lid on the Large container, the small one does not need a lid, make sure you have a decent sized vent hole at each corner of the box. This is called the Hygroscopic incubation method invented by Bob Applegate, it works very well.
Good Luck