[mikeash]

I don't think the payload matters much. Certainly its own weight is insignificant compared to the rocket as a whole. I'm not sure if they might load less fuel if the payload doesn't need full performance, but if so I think that would be a relatively small effect as well.

I didn't find actual TWRs listed even just for the launchers, but you can find the liftoff mass and thrust pretty easily, and just divide.