Our cat is also very greedy and has broken open other feeders in the past (we had to weigh them down with several books). But nothing has ever happened here.
The lid fits tightly and is, in my opinion, also quite odour-proof - so the cats don't even smell the food inside. You can only open the lid through the flap at the back, which I think is also quite difficult for a cat. If yours could manage it anyway, I would just put the machine close to a wall or cover it with tape.
The button for manual dispensing must remain pressed to skip a portion, pressing it once is not enough.

Since our cat respects the flap, I just tested it with my finger. The flap closes again - but since the flap is only made of plastic, nothing happens. But that's more of a problem, and if your cats tend to reach in there, the output gets blocked and the flap no longer closes properly, because grains get stuck in between.
I have to say, though, that the sound is a bit off-putting for our house cat - maybe for yours, too. He runs when he hears the flap, but then only comes to the bowl to eat when all the grains are out. As soon as the food is out, the flap closes again very quickly.

Hope I could help. :)