I don't see why adding +1 to all responses would make any difference to any of the comparisons; it shifts all datapoints equally. (And anyway, log1p(0) ~> 0. The point of using log1p is simply to avoid log(0) ~> -Inf`.)
The explanation by owencb is what I was trying to address. To be explicit about when the offset is being added, I'm suggesting replacing your log1p(x) ≣ log(1 + x) transformation with log(c + x) for c=10 or c=100.
If the choice of log-dollars is just for presentation, it doesn't matter too much. But in a lesswrong-ish context, log-dollars also have connotations of things like the Kelly criterion, where it is taken completely seriously that there's more of a difference between $0 and $1 than between $1 and $3^^^3.
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