Also... get some friends and do both single and group zombie sounds... Groups always sound better than layered singles. And you might also want to play around with this app: http://orfeasboteas.com/dehumaniser/. I tend to process the sound and then layer it against the original for best flexibility.
My suggestion would be to get a bunch of people together and do a voice record session. You can record as a group as well as individuals and then build up a library for you to use. The moaning will be more convincing with a human voice and you can always augment any specific attacks with more layered sounds.
I think you've already hit the nail on the head in your question; just do some moaning, and various types of breathing yourself and pitch that down too; scrap the lion growls! But don't just pitch it down, stretch it too, long and slow.
If you want to layer it up even more though, then you could add some wet slurping squelching sounds etc. for 'freshly ...
The scariest monster I ever created was by granulising baby loughs/crys with ableton inbuilt granulizer/pitch shifting algorithm. Just pitch it down and make the grains short and audible. BrRRIIiiahhhhhriiiaraawwr :)