How can I manage PL/SQL package source at the method level?
Some pondering if you're in fact having a XY problem. YMMV.


  Using an existing utility, is there a way to store package methods as discrete files in source control and deploy them to their package individually?


To me this sounds a peculiar requirement. In database a PL/SQL package is a single atomic unit (in fact there is two units (a specification and a body) but that's irrelevant in this context) that is modified and deployed as a whole.

Let's rephrase the question:


  Using an existing utility, is there a way to store Java class methods as discrete files in source control and deploy them to their class individually?


I'd say that's simply silly. IMO one should treat Oracle PL/SQL source code in the same love than any other programming language source code.

(I'm not ware of such a tool, but you very likely can make that by yourself.)

Your real problem are monolithic PL/SQL packages:


  [...] PL/SQL packages that are large and monolithic in nature, containing a wide assortment of functionality.


That conflicts your parallel development paths.

Reading the fine manual:


  A package is a schema object that groups logically related PL/SQL types, variables, constants, subprograms, cursors, and exceptions.


And finally the root cause:


  [...] because each package requires additional configuration in the ERP suite itself.


IMO tail wagging the dog.

Resolve this problem, refactor your PL/SQL to have a modular structure and your development/deployment conflict problems mostly disappear.

I don't know the "ERP suite configuration" details but I'm positive it's PITA-factor is much smaller than the current mess.