I have BTC in Bitcoin Core, have never claimed BCH. I tried the Coinomi method and it did not work to claim the BCH.
What exactly did you try? And why did you try this already if you still need to move your Bitcoin to a new safe address?
These are the basic steps:
-move all your Bitcoins to a new address
-export the private keys to the Bitcoin addresses that held your coins at the moment of the fork
-sweep the private keys into Coinomi, do this for Bitcoin Cash, Bitcoin Gold and Bitcore