•Tame up a bunch of low level female yutyrannus (I currently have 12).
•Tame at least one low level male yutyrannus for the mate boost (which also increases egg production).
•Tame a low level oviraptor for the egg boost (The oviraptor must be set to wander for the boost to work. You can weigh it down with stone or something so that it doesn't move and you still get the boost).
•Put the yuts around the oviraptor so that they all get the boost and are all mate boosted.
You should get a ton of eggs with this method. The yuts are fairly easy to tame. Just make sure you kill the carnos first so that they don't get in your way. I also like to use the yuts as extra storage for hide/keratin/anything so that I can get as much use out of them as possible.
Instead of trying to remember all the different egg sizes and what they make or combing through your fridges while looking at the app, just read the egg description. It says provides simple nutrition, regular nutrition, exceptional nutrition etc. Which corrosponds with regular kibble, exceptional kibble and so forth.