To my surprise, I quickly succeeded using the jarjar utility, as suggested by CommonsWare.
The key to understanding how to do this was this QA:
Hand Change Jar to Change Package Names
I renamed one of my .jar using the guidelines above, and now they both sit side by side in my project.
I do not want to duplicate SO content, but for completeness I did the following:
Received latest version of jarjar .
Created a configuration file called rules.txt containing one line:
rule uk.co.dog.** uk.co.cat.@1
This is just an example. Given the .jar value with the uk.co.dog.* Package, dog will change to cat . Obviously change this to suit your actual case.
Then use the command line:
java -jar jarjar.jar process rules.txt in.jar out.jar
Where in.jar is the source of .jar and out.jar is transformed.
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