I have the same situation. My brother is tired of hearing my fly fishing stories and wants to create some of his own. He is coming down this weekend to get a crash course in preparation for a trip we are doing to Yellowstone later this month. The only difference being that he has all his own gear already including waders. I plan to take him to the Clinch this weekend (weather permitting) because it will be his best chance at short casts and hooking up. I expect a large crowd there for the holiday weekend, but as I said…..I still think it is his best chance.
There are a few brook trout streams that you and your friend could try but many of them are pretty confined and would make it difficult for a person with no experience casting a fly rod. I am not sure if your friend is coming this weekend or not but water levels will be an issue with the rain we are expected to receive this week regardless of where you decide. Sorry I wasn’t much help but I think your assessment is right. I’ve waded the Clinch with no waders but it wasn’t very fun because of the water temperature. The park may be your only option.