I have a question. I have a dataset with some missing values that were not MCAR. I imputed them with fully conditional specification method iterations. I then executed my analysis on the basis of the imputed dataset. The results of the original model (with missing values: listwise deletion) did not change much in the eventual pooled model. My idea would be to go back the missing values dataset. What do you think?
I think the choice depends on the audience that will read whatever you write.
If they are mostly statistically unsophisticated, I'd say you could use the original data set and put a footnote about how multiple imputation did not change things much. If they are more sophisticated, I'd go with the MI analysis. Even if things don't change "much" they change some and the MI is a better approach.
Also, be careful that you looked at all the output for what changed (or didn't). Not just parameter estimates but their standard errors (or whatever your analysis involves - you didn't say what analysis you did, so it's hard to say what might be affected).