You're not the only one researching this family. There are at least two of us.
I agree with your placement of Tandy (1,2,3). Tandy(2) b closer to 1740, perhaps, since he had a son b ~1761. And evidence suggests he d ~1798, Laurens co SC. Do you have evidence of a Tandy, d 1784?
However, evidence suggests that Tandy(4) "the Pioneer", was b ~1768, son of a William & Sarah. Do you have evidence of a Tandy, b ~1784?
And, since the works of E L Blair and Worth S Ray, many have the mistaken idea that Dr Tandy (your #5) is son of Tandy(4). Evidence shows that Tandy(4) had a son Tandy H Walker, who moved to TX with him, while Dr Tandy was son of another William (& Elizabeth) Walker, and lived in AL.
I also suspect that Tandy(3) had a son Tandy, but without direct evidence, we probably should leave that for another discussion, for now.
I have been trying for some time, to unravel this family, and have been hoping to come across someone else who is actively researching them. I'll collect my notes, and present the evidence I've found so far. There's a lot of ground to cover, though.