I think I figured out how to do this. Trying it now, but it looks like all my DEM pieces are exactly 87,809m x 11,432m so all I have to do is manually enter in the position for each piece using multiples of those numbers, and with the correct offset based on the 4x3 grid these make. I have Parallels (lat) from N36 - N 38, and Meridians (Lon) W112 - W115, which gives me a 4 x 3 grid.
Am I on the right track?