You want a high level oviraptor and put all levels into melee. Melee damage affects the size of area they pick up eggs. Then put your ovi on lowest follow distance, line them up next to a fridge and put railings round them. You can move the eggs to the fridge really easy then not have to worry about the wanderer skedaddling
Everyone needs to know and it is dev confirmed that Oviraptors DO NOT buff chances of mutations or twins or triplets. This is a long going myth that needs to be shut down. Any twins or triplets you are getting is purely coincidence. This was said by one of the devs on twitter!
These guys can steal eggs without aggroing surrounding dinos! You can get easy wyvern and rock drake eggs! Put it in a cryo pod, sneak into a nest, pop it out of the pod and have it set to follow close, run to the other side of the nest and when it gets to the nest it will take the egg. Once it has the egg you can take the egg from it and there won't be any aggro. Just make sure you don't switch the egg out of your inventory because you'll get the aggro then. Rinse and repeat for super easy wyvern and rock drake eggs!