Honestly, I've had way better luck just putting the eggs straight into a container with the same sub/setup I would use for rearing. I keep the eggs/larvae communally for L1 - mid L2, keeping in mind not to let them over crowd. So basically I just bury the eggs in moderately pressed moist oak flake sub.
As far as the actual egg check, I find it helps to have a second container about the same size or bigger than the ovipositing container to move the sub into as you search. You can pretty much just scoop out all of the loose/uncompacted sub from the top; you'll almost never find eggs if the sub is loose. Just to be sure though you can kind of shake the sub out of whatever you're using as a scoop like you're spreading salt instead of just dumping it into the other container. Any eggs will be pretty obvious. They're not exactly small, and even the ones that are stained are bright white compared to the sub.
Once you get down into the compacted sub, I like to incline the ovipositing container by 45 degrees or so and just kind of use my fingers to brush/rake away layers of sub, and push it all down so it collects at the other side of the container, scooping it out into the other container once there's a good bit of it. You just have to be fairly gentle so you don't damage any eggs. You'll get a feel for it pretty quickly.
If your ovipositing container is plastic and flexible enough, you can actually just bend the bottom of the container a bit to sort of "crack" and separate the compacted sub into chunks, which you can just pick up and them gently roll in your hand/fingers to break it all up directly into your other container. I find the sub tends to "crack" along where there are eggs anyway, so you'll likely find some just in the exposed edges. Alternatively, if your ovipositing container is on the small side you can just dump it onto a tarp or something, which makes it much easier to grab chunks to work through.
Sorry if this was rambling; I am excessively tired. Good luck with your egg hunt!