I would advise to be cautious about this. If your team finds they are consistently renaming adapter connections or moving them from one package to another, then there is likely something amiss in the development approach/naming conventions.
Devise a connection naming scheme.
Create a package that holds all your connection definitions. Or if there is a natural segregation to the connections that are needed, use multiple packages as appropriate.
Never put a connection in the same package as “code.” Connections should always be isolated.
Never deploy packages containing connections from one environment to another–e.g. dev to test to prod. Instead, use IS Administrator to define the connection manually in each environment.
One might say “Deployer can deploy connections and update URIs, credentials, etc.” That’s true but I’ve found that to be just as much work as simply defining connections directly in the new environment. Doing it by hand reduces the risk of a catastrophe when prod points to QA or vice versa.
The times when a connection really should be moved/renamed should be so rare that a helper tool isn’t really necessary. Make moving/renaming hard so that it is defined properly in the first place. 
All that said, you’ve layed out the steps for what to do. There are services available for each, though as noted above the getDependents service is not documented and not intended for our use so if you run into trouble, SAG support will not help you.
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