I've noticed that oviraptors tend to glitch out of pens and Dino gates. So I started loading wood til they can't move. Won't help if your trying to get a fertilized egg but will allow there bonus egg production to work without losing them.
Unless you have one of the top 6 eggs listed on this app, stick to small ones. The lighter the egg, the faster they eat it. Unless it’s one of the top 6, they all give it the same amount of points for taming. For example, a Rex egg will tame it faster than dodo eggs, but dodo vs. titanoboa? The titanoboa will take longer to eat, but you’ll need just as many in the end. At least on Mobile. Just get a ton of light weight eggs and go at it.