The question is about marginal effects (of X on Y), I think, not so much about interpreting individual coefficients. As folk have usefully noted, these are only sometimes identifiable with an effect size, e.g. when there are linear and additive relationships.
If that's the focus then the (conceptually, if not practically) simplest way to think about the problem would seem to be this:
To get the marginal effect of X on Y in a linear normal regression model with no interactions, you can just look at the coefficient on X. But that's not quite enough since it is estimated not known. In any case, what one really wants for marginal effects is some kind of plot or summary that provides a prediction about Y for a range of values of X, and a measure of uncertainty. Typically one might want the predicted mean Y and a confidence interval, but one might also want predictions for the complete conditional distribution of Y for an X. That distribution is wider than the fitted model's sigma estimate because it takes into account uncertainty about the model coefficients.
There are various closed form solutions for simple models like this one. For current purposes we can ignore them and think instead more generally about how to get that marginal effects graph by simulation, in a way that deals with arbitrarily complex models.
Assume you want the effects of varying X on the mean of Y, and you're happy to fix all the other variables at some meaningful values. For each new value of X, take a size B sample from the distribution of model coefficients. An easy way to do so in R is to assume that it is Normal with mean
coef(model) and covariance matrix
vcov(model). Compute a new expected Y for each set of coefficients and summarize the lot with an interval. Then move on to the next value of X.
It seems to me that this method should be unaffected by any fancy transformations applied to any of the variables, provided you also apply them (or their inverses) in each sampling step. So, if the fitted model has log(X) as a predictor then log your new X before multiplying it by the sampled coefficient. If the fitted model has sqrt(Y) as a dependent variable then square each predicted mean in the sample before summarizing them as an interval.
In short, more programming but less probability calculation, and clinically comprehensible marginal effects as a result. This 'method' is sometimes referred to CLARIFY in the political science literature, but is quite general.