Not sure if it's been suggested before, but rather than sifting through each and every particular species to see which one has the egg move, it'd be better if there was a filter for the same.
Thanks.
Awhile ago I requested 'Moves' in general be a filter on the GTL, so you'd be able to select the species you want and then the move that you desire them to have.
I believe this to be a better way of handling it, as you have complete control over which moves you'd like to have - not just those obtained through breeding.
We may see such a feature eventually, but I'm not sure as of now.