We're not looking at utimate origins here, just how limestone formed. If Brown has to rely on assuming that God put a lot of limestone in these hypothetical caverns for some reason we don't know then he hasn't got a good explanation for the presence of limestone.
The problem with the CO2 is that Brown describes it as a small quantity in the context of the caverns and then makes it sound as if it were a far larger quantity when it is released into the atmosphere. But he gives no mechanism for producing more. You can't just take "extra" CO2 out of the solution without dealing with the calcium ions.g