Doug,
There is no need to cure the rock in the garbage can at all. You are starting a new tank. If this was an existing tank with fish in it, then I would say yes, cure it. I am not a big fan of curing LR in a garbage can in the dark. IMO it is not really LR any more once you do that except for the coraline and some sponges and bacterial growth. Why kill what you are trying to promote?
Part of the reason for creating a good cycle to begin with in setting up a tank is to be able to have the tank handle a larger bioload at the begining. When this cycle is done, you can add LR to the already baseline established microbiological bed. You will go through a secondary cycle with the edition of the rock but it wont be anywhere near the extreme as if you did not do the preliminary cycle. This will assure that you will keep most of what you paid for on the rock keeping a more diverse ecosystem in the closed system that we call an aquarium.
Also while cycling your tank, dont do any water changes as this will also prolong and weaken the cycling process. This is also one of the drawbacks of cycling with fish.