For the most part, at least. If the edge cases where they differ still feel weird, I can iterate on this further.
The diff is unfortunately a bit impenetrable, because I had to change both the fillGaps and cycleTileSize core algorithms used by the big grid layout. But: the main change of significance is the addition of a function vacateArea, which clears out an area within the grid in a specific way that mirrors the motion performed by fillGaps.
In preparation for adding layouts other than big grid to the NewVideoGrid component, I've abstracted the grid layout system into an interface called Layout. For now, the only implementation of this interface is BigGrid, but this will allow us to easily plug in Spotlight, SplitGrid, and OneOnOne layout systems so we can get rid of the old VideoGrid component and have One Grid to Rule Them All™.
Please do shout if any of this seems obtuse or underdocumented, because I'm not super happy with how approachable the NewVideoGrid code looks right now…
Incidentally, this refactoring made it way easier to save the state of the grid while in fullscreen / another layout, so I went ahead and did that.