Yes, the fit was done in the logP vs t domain. I have a bit more of an exploration of the difference coming in a long post I didn't manage to finish last night, but hope to tonight.

Also BTW (since it's taking a little while creating an account at peakoil.com) I wanted to make a comment on your post over there adding random Gaussian noise and then doing kind of a bootstrap type error estimation. I think that approach will underestimate the size of the error bars because you're not taking account of the structure of the errors. I don't know if the residuals of the various models are just auto-correlated or actually systematic, but they are very clearly not iid random. You might want to plot the autocorrelation r^2 as a function of lag in the residual time series from your model fit. If the residual autocorrelations fall off exponentially with lag, IIRC, very roughly you can consider that you have one independent observation per lifetime of the falloff.