Let me try to answer, but if I'm off-base, perhaps you could provide more details.
What I think you are saying is that you have some project management tools you use for work and you find yourself adding tasks and projects to both this system and your own GTD system.
As long as the work system is adequately capturing everything you need to know to get that project off your mind, there is no need to also add these things to some other system. In my case, I have responsibility for about 500 projects that my staff manage. Very few of these are in my GTD system. Occasionally, when there is something I need to keep an eye on particularly I will add a task for me or a waiting-for I have requested, but for the most part, they live in their own system. If I needed a reminder to interact with the system (which I don't - being at work is reminder enough) then I could put something like "Work in System X" on my task list.
Your GTD system is for you. Things you need to do. Projects you want to keep an eye on. Things you are waiting for. Your project management system is designed for your team at work. The purposes are different but there should be minimal overlap. Sure, you may want to list the project on your GTD project list but that is a one-liner - no need to repeat the details.