If I've understood correctly what you're saying, you seem to be implying that if 'over-refining' (whatever that means) at some point produces an increase in Rfree along the trajectory then one should stop refining at that point. However this is tantamount to using Rfree as a convergence criterion! The whole point of Rfree surely is that it has absolutely no say in the decision when to stop refinement (otherwise it's no longer 'free').
The target of refinement is the maximum of the likelihood, not any of the R values (clue: it's called 'maximum likelihood refinement', not 'R-value refinement'). So it's actually completely irrelevant whether the R values go up or down during the refinement, since they are not the functions being optimised. Since the functional dependence of the R values on the parameters is quite different from that of the likelihood (for one thing the conventional R values take no account of the weighting), there's absolutely no reason why the R values should slavishly follow the likelihood in its upward trend.
So the only thing that matters is the R values at convergence. Convergence as well as optimal agreement with the model is achieved when the likelihood is a maximum under the given starting conditions, and if you were to monitor the likelihood you would see it increasing monotonically: the optimiser does not permit a downward step! So 'over-refinement' by the definition I have understood is impossible! (or maybe I have misunderstood the definition: perhaps someone could define what they mean by 'over-refinement'?).
This of course doesn't mean that if you had started with different conditions (e.g. a different model, parameterisation, weighting scheme, etc.) then you mightn't have obtained better agreement between the model & data at convergence. If under different starting conditions you obtain a higher Rfree at the maximum of the likelihood then it's likely you have overfitted (not over-refined), i.e. you are fitting the parameters of the model to some degree to random errors in the data. Overfitting is determined by the starting conditions (mainly the observation / effective parameter ratio), not by the conditions at convergence. The Rfree value at maximum likelihood convergence is a measure of the overfitting that was already inherent in the starting conditions: if you stop refinement before convergence Rfree will most likely not give you a true measure of the degree of overfitting.
