I place eggs (on tile, or what ever u have) in a plastic soup container. Cuts large holes in cover of soup container for water exchange. Place eggs into soup container with tank water, cover container. Then do a 2-3 gl WC and use the old tank water in a bucket to transport the soup container with the eggs....this way you have eggs secured in soup container with a large amount of water around it to keep parameters stable and prevent and sudden movements.
I actually remove the 2 gl of old tank water first, then move the eggs second, then refill tank lastly. This keeps the eggs in the same water the whole time.
I hope this makes sense.