A sump will undoubtedly be your best option in the long run.

Not much bacteria will come from the 'cycled water', mostly waste in there actually. You said you are moving established rock, so that is going to be key to the cycle in this case. Even with the LR you are bringing over, the tank will still cycle until it establishing an equilibrium between the waste being provided and the bacteria to consume it. Some waste will be in the form of die off with the LR you are bringing and some of it may come from the established water you are using. I don't use established water, just LR to seed. I don't really see any benefit in doing so. You'll bring bacteria and pods over on the LR. I wouldn't expect it to cycle any quicker than any other new setup that cycles off LR.