The last remaining problem (that I know of) with moving and copying of groovy compilation units are that import statements are not properly updated.
For Java files, an import rewriter is used, but this does not work for groovy files. Perhaps, we can make a change in the import rewriter to delegate to a groovy version when required. We already have a "groovy organize imports" action. This can be refactored a bit and moved from UI to core and then this can be used to rewrite import statements.