Contrary to urban myth, all Damsels are resistent to the ammonia/nitrite cycle. (Blue) chromis in my experience actually does worse than some bigger, tougher species like triggers, and even not as well as some shrimp like coral banded during tank cycling.
The domino and 3-stripe (same family) are tougher than chromis during tank cycling in my experience. The problem is that both are among the most pugnacious and territorial of marine fish and will not let new fish be added after cycling, unless you are including even tougher fish. A 3 stripe damsel that's learned he's king of his reef during cycling will make you wish you could rent a barracuda for a day to save you the grief of catching the obnoxious thing.
There also isn't a law that says your fish have to endure toxic ammonia levels during cycling. At any point that ammonia levels get really high you have the option of doing a water change to lower it. Having ammonia levels off the charts won't speed up nitrite reduction, nor cycling, so it's not necessary to keep the levels high.
This is a bit more theoretical and not to be tried at your point in a live tank, but I have cycled starter tanks with LR
in just over two weeks with a cap (1/2 oz) of ordinary ammonia added over a period of a few days. Might be cleaner than messing with dead shrimp in case you just can't get damsels to live.