I would put in about 2 cups and if the "bleaching effect" is visibly effective that would be enough. If not, add some more. You're going to dilute it with hose water after a day or so so there is no such thing as too much. And bleach is cheap. It's just that it doesn't take much and you can see it work.
Forty years ago we would remove and bleach the coral decorations (equivalent to live rock) occasionally just to brighten up the tank. Most aquariums were fish only. We let the coral soak in bleach, then fresh hose water, and then sun dry. Back into the tank it went and nobody in the hobby warned against that. Nobody seemed to get any bad results.
I know times have changed and people are more careful now. But, with all the advancements in the hobby, fish still die and corals don't make it. I would never "attack" my live rock if I could solve my problem another way, but in one of my tanks I have a bubble algae problem unlike anything I've run into before. I regularly remove one or two rocks, that don't have coral or anemones on them and either bleach or peroxide treat them, rinse, soak and return to the tank. No invertebrates are in decline from the process, not even the snails and shrimp that go immediately to check out the returned rocks. I don't do many at a time.