Illustrator :: Hide / Remove Pesky Negative Space Voids

We've all seen this:
 
Adding strokes to an object, often text (in this case outlined/expanded text), and there develops little unsightly "negative space shapes".
 
The white stroke has an Offset Path added to it.
 
How to dynamically rid an object of these? Tried drawing little paths over them, grouping them with the compound text path and using Pathfinder > Add effect . . . but nope.

The workarounds are obvious -

1) Expand everything, delete the unwanted bits.  
2) Draw solid paths over the negative spaces that match the bg, like the pic below: