I have a general question about the design of JavaScript Libraries.
I am trying to consolidate common methods into one js file so they can be reused by different scripts
I would recommend you to follow the Module Pattern in JavaScript instead of following JSON's pattern strictly. Your subgroup is actually referring to sub-modules. Take a look at the following excellent article:
Ben Cherry's JavaScript Module Pattern In-Depth
Other resources you should probably go through:
There are problems with the module pattern. See http://snook.ca/archives/javascript/no-love-for-module-pattern. I used to use it before but stopped. Now I just tend to keep it simple. If you really want sub-namespacing you can make a simple namespace function for the job.
See http://blogger.ziesemer.com/2008/05/javascript-namespace-function.html