First, you need to unmerge all cells in the range A3:L122. I think you can actually do this without any real damage to your formatting.
I have shifted your data one column to the right and added a formula in column-A that I think allows you to sort while keeping the four associated lines per load together.
The formula in column-A generates a sort key. The formula needs to be sensitive to the row on which it appears as the relative position of the status field and load number field changes depending on which row in the group of 4 rows per load that we are trying to reference it from. We also need to keep the four rows per load together and in the right order when sorting. These constraints drive the relative complexity of the sort key formula.
Here's the formula in A3. It is copied down to A122
When sorting your sort range needs to be exactly A3:L122
See if this approach is on the right track. If it is then the final step would be to decide what to do with the sort field - I'm sure you don't want it cluttering up your user interface.
Attached is your modified workbook implementing the above.