With this specific request, there may be some manual labor needed behind the matter.
Here's how I would personally handle it:
-Create a smaller extract (like you mentioned) using filters.
-Publish smaller extract
-set this extract on a refresh scheduler
Now if a column is added you may have to come back to the extract and add it- but you can test it out to see if the extra column pops up as well
Couple ways of making the smaller extract:
Hopefully this helps!