I agree with Big Jim, I don't see how the Tribal Police have any jursidiction in non-tribal areas.
One thing that hasn't been suggested, that I really think needs to be done, is to tell your story to WDFW enforcement. I don't know the regs or laws here. I'm sure anywhere in Hood Canal is a "Usual and Accustomed Fishing Area", but Hoodsport is not on Tribal land. So I think, like any fishery, it is regulated by WDFW--in other words, they have an announced quota and seasons, etc. WDFW is responsible for regulating potential gear conflicts, as well, such as buffer zones between pier and boat fisheries (Elliot Bay), having separate seasons for sport and net fisheries (Lk. Wa Sockeye). I have EMAILed enforcement when reporting poachers and have gotten responses back to them.
I would suggest you provide WDFW a detailed EMAIL of the encounter, including (especially) what the Tribal cop told you. Also, inquire what are the laws that govern these situations, so they will have to respond back to you. If there is going to be a gear conflict between two different fisheries, such that one prevents the other from fishing, there have to be advanced announcements. If not, they had no right to interfere if your were there first.