Sorry for the late response, I have been busy.
The reason that sizes are off on your site is mainly because the tiles are switching to the small screen template. It takes the size of its container to decide if it should take the small screen template or the big screen template. Simple fix: set the small screen template size to 0 (in the WP Tiles settings screen).
However, for what you want the best approach would probably be to put a filter on the tiles themselves (in just 1 container) and performing a query that puts the right posts at the right spot, in a similar fashion as the WP Tiles menu gist.
Or, I just realized. Do you only want to show one row of tiles? If so, you might be better off using some simple css instead of WP Tiles (as WP Tiles is a bit overkill for that)..
Let me know how it works out!