Views "post" filter (complex query)
hook_views_pre_render() would enable you to filter out results after the query has already been run. Keep in mind that the results that are filtered out are still part of the query, with all the performance ramifications of that. Putting that in a custom module would be how I would do that.

If you don't want a view that's just a filtered version of the IsImportant == TRUE view, you could clone the first view and create a similar one whose only difference is that it returns four more results than the IsImportant == TRUE view. You could then add whatever filtering logic you want, and then limit the display to a certain number of items before rendering.

You may also want to take a look at the Peek Summary module, since it gives some further granularity to number of results returned beyond what Views alone offers.