It took 2 years for me to run into the scenario, but it finally happened. I need to maintain the base customization of my project used by all clients. Then I need to add a field to a client specific customization that adds a field to a screen already customized in my base customization project.
A quick search of StackOverflow yielded the answer. Simply set the order that you wish to apply the customization projects by setting the Level field of the Customization Projects screen.
In both projects, I have customized the Sales Order Entry (SO.30.10.00) screen. When publishing, the lack of setting levels results in a validation error reporting conflicting changes to the same screen.
Simply adding the priority via the Level field resolves the conflict by telling Acumatica which customization takes priority.