Replication filtering can only be configured after read-replica is already created - resulting in replicating unwanted tables that cannot be dropped

According to the AWS docs, I can set-up filtering for read replicas.

This works, but not as expected; because setting up the required parameter group with the replica can only be done after creating the replica. This means that once the read-replica is made (with the added overhead of cloning the unwanted tables), the new parameter group can be installed to prevent replicating unwanted tables. At that point in time however, the unwanted tables are already created and filled with now stale data. Since it is a read-replica, these tables cannot be removed.

I did find a topic somewhere that advised creating the database through the API. I also tried this route, but it results in the following error:

An error occurred (InvalidParameterCombination) when calling the CreateDBInstanceReadReplica operation: A parameter group can't be specified during Read Replica creation for the following DB engine: mariadb

The only thing I have not tried is figuring out if the read-replica's read-only state can be temporarily changed to be able to write, drop all the unwanted tables, and reconfigure the read-only state. But not only do I know if this is possible, it seems very prone to error.

p.s. The reason I need this feature is because I have several applications that have to make use of the same database, each with a lot of traffic. But one of the applications records a very large amount of history in a couple of tables that do not need to be replicated.