[amelia] combining imputed data for more complex models

I have a question about combining imputed data from Amelia. I understand the rationale for running your end analysis on each imputed data set separately, and then combining the model results. However, what if your analysis is more complicated than a simple LM? For example, for my analysis, I am using imputed data sets (5) of time series variables (12 independent water quality variables, all time series, and 1 dependent time series). I am decomposing each series using loess and extracting the trend only. Then, I am using prewhitening and cross correlation to identify lags of variables that may be useful predictors. Finally, I am differencing each series and creating and comparing ARIMA models with external regressors to find the best model. I am having a hard time understanding how going through each of these steps with each imputed data set separately (and trying to combine the best models) is not going to create more variability and decrease the confidence of the model compared to averaging the imputed data sets before doing any analysis. In short, if my imputed data sets are not "that" different, and the range of values for each of my predictors is relatively small, could it possibly be better to average the data first instead of trying to combine the best model from each? I would greatly appreciate any comments or suggestions. Thank you for your help.