We use the rabbit waste...directly in the gardens now, the plants LOVE it.
The chicken waste I compost in a barrel composter (few weeks) then use it, never had a burning issue.
I too read so much conflicting info I usually try it out on test areas 1st lol
How's that composter working out for you? I'm thinking about building a double barrel composter in the not too distant future to handle the coop bedding. I am hoping to turn out a high grade compost quickly. The rest of the garden waste goes in the bins, takes about a year to break down as I'm not to attentive to them. The piles only get turned when I move them from one bin to another.