Don't show Header view after clicking next on pager
I have an idea:

Create a third view that's a page showing articles with an offset of 16 (so it skips the 4 and the 12).  Call it 'older articles'.

Then instead of a pager, have a 'more' link under your view of 12.  It's important, in the 'Advanced' section of the view, to set the more link to go to that new views page (older articles).  The older articles page can then have its own pager!!!  But the initial articles page -- the landing page -- can just have a 'view more' link so it can hop over to the older views altogether.

Would that be sufficient?