We also have ended up doing the same thing as what @julian said.
Also, the settings of the new database must match the original (Encrypted, AllocatedStorage, EngineVersion, Family, etc).
is important, as it caused us a bit of a headache!
Re: “We’ve had some problems updating the parameters afterwards,” we have ended up modifying the RDS instance directly rather than through convox, which has put the convox vs. real settings out of sync – not ideal, but managing the DB directly through the AWS console is not a big deal for us. Could probably cause issues down the line though, so take with a grain of salt!
We successfully did this replicating some production instances, (wait for it to replicate, then switch over our services to use the new postgres instances, then kill the old instance).