I agree with Sunthud. To elaborate, the point of equating measurement parameters is not so that you can compare measurement parameters across groups/times. Rather, latent parameters (means, SDs, factor correlations, regressions between latent variables) can only be meaningfully compared across groups/times if the (unstandardized) measurement parameters are equal. If you are merely interested in comparing measurement parameters across groups, you do not need to compare them -- fit the configural model (allowing loadings and intercepts to differ between groups) and compare your completely standardized estimates, which will tell you how much more strongly each item is related to the common factor in one group than another. You can still make this comparison after constraining the loadings to equality, allowing latent variances to differ across groups (which would already be the case if you use a marker variable to set the scale), because there is no stipulation that equal factor loadings implies equal item-factor correlations (i.e., standardized loadings, unless an item measures more than one factor, in which case its loadings are semi-partial item-factor correlations).
If you want to constrain standardized factor loadings, that would only be possible if not only the factor loadings themselves were equivalent, but also the factor variances and residual variances. To implement this constraint in practice, as you seem to have noticed, you would need to start by making the indicators' total variances equivalent across groups (e.g., by transforming raw scores to z scores), then constrain all parameters across groups. In this case, you are completely equating all parameters across groups, in which case you may as well just analyze the data as a single group, ignoring any between-group differences. But if you are interested in comparing latent regressions or means across groups, then equating unstandardized measurement parameters is necessary (at least one per factor), whereas equating standardized measurement parameters has nothing to do with that goal.
Terry