A pin works well for removing white eggs, you can get the close ones this way if you are inclined to do so.
The white ones with fungus are usually attacked by bacteria first. Bacteria is faster growing than fungus, the fungus is secondary. Fungus generally will not spread to viable eggs, bacteria can. This is why cleanliness is important in a hatching situation. I don't try to remove white eggs from angel spawns, and have eggs that are right next to fungused eggs hatch out just fine.
Sometimes parents need a few tried to get things right, sort of like first time parents compared to parents having their third kid. I lucked out with my apistos, they got it right from the start.
When hatching spawns, knowing that bacteria can be a problem, I've found adding a couple things besides meth blue helps. I go with 7 drops per gallon meth blue, 3 drops per gallon Maroxy, and a drop or two per gallon acriflavin. I start with 50% daily water changes on the fourth day after spawning.