Because the adults are eating the eggs straight away I would do the following.
If eggs have been deposited on plant leaves, remove the leaves without actually touching the eggs. The same goes for eggs deposited on other removable objects. Newly laid eggs are quite delicate and although they are handleable they are sensitive and can be damaged by the salt and oil on your skin.
If the eggs have been deposited on the tank sides can be carefully removed using a razor blade.
Rather than a net, I would use a floating container with 1 1/2" of tank water and add a air stone. This is better for treating with anti fungus treatment and here I would recommend Primafix, although the best anti fungal treatment for eggs that I know is the cones from the Black Alder tree (Alnus glutinosa). Not knowing your location I cannot tell you if they are available in your area.
As Jollysue said any eggs that turn white are likely to be infertile and should be removed. The fry will start to emerge from the eggs after about four days and are free-swimming in about two more days (this time may vary, but for most Cory species this is about right). You will see that their fat bellies will have disappeared. This is also the time to start making regular daily 75% water changes using water from the main tank.
The fry when free-swimming will be large enough to take micro worm, wetted powdered flake food or crushed Tetra Tabimin. I have found Liqifry unsuitable for all but the tiniest of Cory fry. After a couple of days the fry will be large enough to take newly hatched Brine shrimp.
Ian