Okay, so you were using each cup as a mini-pot. I think the biggest challenge with that is regulating the temperature, since there's so little water in ratio per egg, adding the eggs create a bigger temperature change to the water than it would in the heat sink that a larger pot of water creates.
Then as far as sticking goes, that spillover spreading white around, well, we know eggs are one of the biggest challenges for non-stick surfaces, without the extra lubricant of oil (or butter, ideally). I would also speculate the lower temperature used for poaching makes it stick more, but that's just a guess.
I don't use them but the specialty egg poachers more resemble the technique for steaming, where a container with the eggs is placed in a bath of simmering water, no direct water contact with the eggs, which accomplishes cooking at the lower temperature than frying. I thought that was what you were trying to reproduce. And even those often recommend a non-stick spray first.
When I poach I just bring a pot half-full of water to a simmer. Add a little salt and some red or white wine vinegar to help firm up the whites. Instead of cracking the egg directly into the water, crack it into a small bowl and then gently slip it into the water (pouring it out of the bowl right at water level). Let it simmer for about 3 minutes (the timing is the trickiest part) then gently remove it with a slotted spoon, place on a paper towel, gently pat dry, then transfer to whatever meal you're assembling. I can easily do 2 or 3 at a time in a medium pot and still keep them separate.
There's a "vortex" method where you first swirl the water then slip the egg into the center, supposed to hold its shape better, but it limits you to one at a time and frankly when I've tried it the results were about the same. Fresh eggs hold their shape better than older ones (while older ones peel easier when hard boiled).
I hope that's the sort of feedback you were looking for.
But I love me a good poached egg. Ideally the white should be firm but the yolk still liquid, a little thicker than full-raw runny, which is why the timing is the trickiest part. IMO the browning on fried or scrambled eggs is undesirable (while The Wife likes her SSU eggs as crispy on the bottom as possible). To avoid the browning I fry on low, usually turn off the heat on scrambled as soon as I add the eggs, but poached never has any browning...
Now you've made me want to go poach some eggs.