Replace last item in a Views grid of images
But is there no way to actually get it into the grid in html from the
  Views UI?


As I can see thare is no way for that in views UI.

But here are possible custom solutions:

Solution1


Add "more link" in PAGER section. Than specify link in 'Link
display' section under ADVANCED.
Style your link with css


Solution2
Add new views row in [hook_views_pre_render][1]

Solution3
Add new views row in custon views template