In short it is possible, yet is there a better way to do it than how I have.
To accomplish this I set the min/max tile constraints of both Minimized and MinimizedExpanded to 0, set all InterTileSpacing for Maximized mode to 0, and set the ShowTileAreaSplitter to false.
This allows only the maximized tile to be seen, yet there is a slight space to the left of the tile where the tile area splitter and minimized tiles would have been. This results in an ugly shift of the right side of the maximized tile.
To lessen the impact to the user I have moved the maximized tile to the top, so the ugly shift and extra space is added to the bottom of the tile.
I would like to remove this space entirely and prevent the shift from happening, could you please advise on the best way to do this. Thanks!
Update: Success
I finally figured out a simple combination that works:
My mistake was the Style for my Tile had a top level Border, and I was setting the Visibility of the Border to Collapsed. You need to set the Visibility of the Tile and then it almost works, just one pixel is left. Setting InterTileAreaSpacing to 0 solves this.
Collapsed Tiles ignore the mix height/width tile constraints, which surprised me, I figured the TilesPanel would still reserve the min height/width.