What would be the best logical way of configuring 2012 SSIS project using the Project Deployment Model?
Consider a scenario of an SSIS Project
From my reading of your question, you have 3 separate servers to deploy to, each with it's own instance of the SSIS Catalog. You do not want a single server to execute for multiple environments. For that scenario, user756519's answer is of little use unfortunately - 10 out of 10 for effort though.
I would ignore the "Environments" setup in SSIS. This is for managing multiple environments on a single SQL Server instance.
Instead I would:
You can now continue to develop and deploy your project to each environment. No further maintenance is required, unless you add/delete/rename a Project Parameter. When any package is executed on each Environment/server, it will follow the configuration set via SSMS