Once you factor in the infinite number of monkeys, every novel in existence will not only be written, it will be written an infinite number of times.

You don't need an infinite number of monkeys to ensure that. The cardinality of an infinite collection of 2-tuples (monkey, char) is the same as the cardinality of an infinite sequence of characters, just as the cardinality of the rational numbers is the same as the cardinality of the integers.

And in a countably infinite sequence of uniformly random characters, there is no assurance that any particular finite sequence will occur only a finite number of times.