A frame number is a good idea, I think. 
However, I am rendering shadows, so as you say, that perhaps won’t work. But see below…
As I said above, I’m not using instancing, so I’m happy to leave it broken for this project. If a later project calls for it, I can perhaps revisit the problem–presuming that subsequent changes to the engine between here and there don’t obviate doing so, of course.
Something along these lines occurred to me after I posted–although I didn’t at the time know enough to have much more than an inchoate concept. I suspect that this may actually be a better idea.
What about this: use a boolean, as mentioned above. While traversing, set the “hasBeenRenderedThisPass” flag to “false”–this is the step at which it’s cleared. In CullBin*–“addObject” looks like a good spot, intuitively–the flag is checked. If it’s “false”, the object is added, and the flag is set to “true”. Otherwise, skip the object and move on.
You mentioned rendering the scene multiple times; when doing so, is the scene graph traversed multiple times? I would imagine so, as different views would result in different culls. If so, and I’m not much mistaken, then this version may well work with multiple renders, as each subsequent traversal clears the flag. If not, it remains an issue…
What do you think?