Hey!

What setup are you using?
In mythic+ I would not step on the eggs more than necessary, and then I have a team with 5 tanks. Having a healer or vulnerable dps step on eggs could probably lead to hatchlings killing that character.

As a melee team, when backdraft hits I just position my team so that they have a lot of room to get pushed back to without having any eggs in that direction. While running towards the boss against the wind, I can continue some dps and all healing.

If you are using a team with a healer that requires standing still to heal, I guess it counts as standing still if you are not moving towards the wind, and are being pushed back?
If that is the case, my tip would be to just position the team so they have a lot of ground to clear before hitting any eggs. And then do whatever you have to for keeping the team alive and fighting the push back at the same time. Dealing with the hatchlings seems troublesome, especially if you only are not a team made up of tanks.
Also I' think the eggs respawn, so being in that area longer periods would mean having a bunch of whelps constantly.