Thanks a lot for provided scene. The "lack of diversity" is because of to the way how the Distribution Map is used in combination with UV mode. Actually, all faces are sharing the same UV coordinates, so just one item is placed to that position in UV space.
Please, feel free to check attached scene with proposed solution. There is UVW Unwrap modifier applied with "packed UVs" to a rectangular grid and than Tiles map with corresponding number of tiles controlling the distribution for that Map Channel. This way each placed item is not sharing the position in UV space with any other item and it's calculated independently.