You don't want to cure your rock, what you want to do is cook it.
Curing is typically done with live rock. You can expect to get some die off so we cure it by removing the dead sponges and other stuff so it doesn't decay in our tanks. This isn't the situation you are in. And yes.. I know.. people use the wrong terms for this all of the time.
What you are starting with is dead dry rock. I would say this video might help
https://www.reef2reef.com/threads/video-cooking-live-rock-not-curing.276079/ but it doesn't exactly apply to your situation either.
Muriatic acid is a common choice for people to use. The only real downside is that it not only dissolves the organics, but it also dissolves the rock itself. I guess another downside is that it is fairly dangerous to work with, especially if you use vinegar to clean, also. Bad things happen when they mix.
Bleach is another popular option to kill any organics, but drying it out like this should make that a non issue.
I think I would go the vinegar route. It's relatively cheap, safer to work with, doesn't dissolve as much of the rock (although it will dissolve some) and doesn't hurt anything even if you don't rinse it well enough. It's going to take a lot of vinegar but I would try to use it straight so it works faster. Let the rock soak in the vinegar until it stops fizzing. You should get a thick foam on the top of the tub you soak them in. Just skim that off. Once it stops foaming (3-8 hours) I would rinse it off and fill the tub with heated salt water and a powerhead. Let that run for a day or two. If the water looks nasty you can run a skimmer to help if you have one. You can test the water for phosphates at this point if you want. Believe it or not, if you don't dry the rock at this point it will actually help reduce your cycle time.