To quote myself, "If you can think of a way to be more convincing by presenting evidence against the desired conclusion, please let me know. I'm the only one I can safely say is impressed by such acts." Though, naturally, writing that un-convinced me of it. I can think of several examples of the "It's true that, but..." construction. There's still some problems with how it's carried out but I'll leave that as an exercise for the reader.
It made me realize something else, too. If being balanced is good, why not take the limit? Why not supercharge it?
New Goal: debate by stating all the relevant evidence I know, for, against, and confusing, about the dispute in question. Completely ignore time/length constraints and convenience. See what happens.
(What I'm posting later today also helped, as I made conscious and explicit what I think happens when I examine an assumption and really try to settle it. Specifically how the evidence is distributed across conclusions.)